资源简介

7．1.1　两条直线相交
1.理解对顶角、邻补角的概念．2．探索并掌握对顶角相等的性质．3．通过在图形中辨认对顶角、邻补角，培养学生的识图能力．
知识点一　邻补角的概念
1．如图，∠AOC和∠AOD有一条 ，它们的另一边互为 (∠AOC和∠AOD互补)，具有这种位置关系的两个角，互为 ．
练习1　(教材P2探究变式)在下列各图中，∠1和∠2互为邻补角的是(　　).
A． B．
C． D．
知识点二　对顶角的概念及性质
2．(1)如图，∠AOC和∠BOD有一个 ，并且∠AOC的两边分别是∠BOD的两边的 ，具有这种位置关系的两个角，互为 ．
(2)互为对顶角的两个角 ，即 ．
练习2　(教材P2探究变式)在下列各图中，∠1和∠2互为对顶角的是(　　).
A． B．
C． D．
知识点三　运用邻补角、对顶角的性质进行角度的计算
练习3　(教材P3例1变式)如图，直线AB，CD相交于点O，∠AOC ＝ 85°，OE把∠BOD分成两部分，且∠BOE∶∠DOE＝2∶3，求∠AOE的度数．
知识点四　利用邻补角、对顶角的性质解决实际问题
练习4　为测量古塔的墙底角∠AOB的度数，小颖、小明两人的测量方案见下表：
小颖的方案 小明的方案
分别作AO，BO的延长线OC，OD，量出∠COD的度数，就得到∠AOB的度数． 作BO的延长线OD，量出∠AOD的度数后可通过180°－∠AOD得到∠AOB的度数．
下列判断正确的是(　　).
A．小颖能得到∠AOB的度数，小明不能
B．小明能得到∠AOB的度数，小颖不能
C．两人都能得到∠AOB的度数
D．两人都不能得到∠AOB的度数
eq \o(\s\up7(),\s\do5(　　　　　　　))
基础巩固
1．下列各图中，∠1和∠2互为对顶角的有(　　).
　 eq \o(\s\up7(),\s\do5(①))　　　　 eq \o(\s\up7(),\s\do5(②))　　
eq \o(\s\up7(),\s\do5(③))　　　　 eq \o(\s\up7(),\s\do5(④))
A．0个　　　　　 B．1个
C．2个 D．3个
2．如图，直线AB，CD相交于点O，OE平分∠BOD，若∠AOC＝40°，则∠COE的度数为(　　).
A．145° B．150°
C．155° D．160°
3．已知∠1与∠2互为对顶角，∠2与∠3互余，若∠3＝50°，则∠1的度数是(　　).
A．40° B．90°
C．135° D．40°或140°
4．如图，在灯塔O处观测到轮船A在北偏西66°方向上，轮船B在OA的反向延长线上，轮船C在灯塔O的东南方向上，则∠BOC的度数为(　　).
A.45° B．31°
C．24° D．21°
5．如图，晓丹家有一个破损的扇形零件，晓丹利用图中的量角器量出这个扇形零件的圆心角的度数，那么这个破损扇形零件的圆心角的度数是________．
能力达标
6．如图，直线AB，CD相交于点O，OE平分∠BOD，OF平分∠COE，且∠1∶∠2＝1∶4，则∠COF的度数为________．
7．如图，直线AB与CD相交于点O，OC平分∠AOM，且∠AOM＝90°，射线ON在∠BOM内部．
(1)求∠AOD的度数；
(2)若∠BOC＝5∠NOB，求∠MON的度数．
挑战创新
8．(跨学科融合)将一根木棒放入盛有水的玻璃杯中，一头露出水面，一头浸入水中，我们可以发现浸入水中的部分“变弯了”．它真的变弯了吗？ 其实没有，这只是光的折射现象，即光从空气斜射入水中，光线的传播方向发生改变．如图，假设一束光AO射入水中，在水中的传播路径为OB，∠1与∠2互为对顶角吗？如果不互为对顶角，如何比较它们的大小？7．1.3　两条直线被第三条直线所截
1.理解同位角、内错角、同旁内角的概念．2．识别同位角、内错角、同旁内角．
eq \o(\s\up7(),\s\do5(　　　　　　　))
知识点一　同位角
1．图中的∠1和∠5，这两个角分别在直线AB，CD的同一侧(上方)，并且都在直线EF的同侧(右侧)，具有这种位置关系的一对角叫作 ，像这样的角还有 ．
练习1　(教材P7例3变式)如图，属于同位角是(　　).
A．∠1和∠3 B．∠2和∠3
C．∠1和∠4 D．∠1和∠2
知识点二　内错角
2．图中的∠3和∠5，这两个角都在直线AB，CD之间，并且分别在直线EF的两侧(∠3在直线EF的左侧，∠5在直线EF的右侧)，具有这种位置关系的一对角叫作 ，像这样的角还有 ．
练习2　(教材P7例3变式)下列四个图形中，∠1和∠2是内错角的是(　　).
A． B．
C． D．
知识点三　同旁内角
3．图中的∠3和∠6虽然也都在直线AB，CD之间，但是它们在直线EF的同一旁(左侧)，具有这种位置关系的一对角叫作 ．像这样的角还有 ．
练习3　(教材P7例3变式)如图，下列各角与∠B不是同旁内角的是(　　).
A．∠BAE B．∠BAD
C．∠C D．∠BAC
知识点四　熟练判断两个角的位置关系
练习4　(教材P7例3变式)如图，下列结论中错误的是(　　).
A．∠1与∠2是同旁内角
B．∠2与∠5是内错角
C．∠1与∠6是内错角
D．∠3与∠5是同位角
eq \o(\s\up7(),\s\do5(　　　　　　　))
基础巩固
1．如图，两只手的食指和拇指在同一平面内，它们构成的一对角可以看成是(　　).
A．对顶角 B．同位角
C．内错角 D．同旁内角
2．如图，下列说法正确的是(　　).
A.∠1与∠2是同位角
B．∠1与∠3是同位角
C．∠2与∠3是内错角
D．∠2与∠3是同旁内角
3．如图，下列说法错误的是(　　).
A．∠3和∠B是同旁内角
B．∠A和∠C是同旁内角
C．∠2和∠3是内错角
D．∠1和∠3是同位角
4．下列各图中，∠1与∠2不是内错角的是(　　).
A． B．
C． D．
5．如图．
(1)∠1与∠3是直线AB，AF被直线________所截构成的________角；
(2)∠2与∠4是直线________被直线BC所截构成的________角；
(3)图中∠5的同旁内角有________个，它们是________________；
(4)直线ED，BC被直线AB所截，则∠1与________是同位角；
(5)直线ED，BC被直线AF所截，则∠3与________是内错角．
能力达标
6．下列各图中，∠1与∠2是同位角的是(　　).
A． B．
C． D．
7．如图．
(1)∠1与∠2是________角，它们是直线________被直线________所截而得到的角；
(2)∠3与∠4是直线____________被直线________所截而得到的角；
(3)直线AB，BE被直线AC所截而成的内错角是____________，同旁内角是____________；
(4)同位角共________对，内错角共________对，同旁内角共________对．
挑战创新
8．如图，直线CD与∠AOB的边OB相交．
(1)写出图中的同位角、内错角和同旁内角．
(2)如果∠1＝∠2，那么∠1与∠4相等吗？∠1与∠5互补吗？为什么？7．1.3　两条直线被第三条直线所截
INCLUDEPICTURE "学习目标上.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET
1.理解同位角、内错角、同旁内角的概念．2．识别同位角、内错角、同旁内角．
eq \o(\s\up7( INCLUDEPICTURE "知识梳理.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET ),\s\do5(　　　　　　　))
知识点一　同位角
1．图中的∠1和∠5，这两个角分别在直线AB，CD的同一侧(上方)，并且都在直线EF的同侧(右侧)，具有这种位置关系的一对角叫作同位角，像这样的角还有∠2和∠6，∠3和∠7，∠4和∠8．
INCLUDEPICTURE "25SX-40.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40.TIF" \* MERGEFORMATINET
练习1　(教材P7例3变式)如图，属于同位角是(　C　).
INCLUDEPICTURE "25SX-42.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-42.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-42.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-42.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-42.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-42.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-42.TIF" \* MERGEFORMATINET
A．∠1和∠3 B．∠2和∠3
C．∠1和∠4 D．∠1和∠2
知识点二　内错角
2．图中的∠3和∠5，这两个角都在直线AB，CD之间，并且分别在直线EF的两侧(∠3在直线EF的左侧，∠5在直线EF的右侧)，具有这种位置关系的一对角叫作内错角，像这样的角还有∠4和∠6．
INCLUDEPICTURE "25SX-40+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40+.TIF" \* MERGEFORMATINET
练习2　(教材P7例3变式)下列四个图形中，∠1和∠2是内错角的是(　B　).
A． INCLUDEPICTURE "L26CGD7SX6.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6.TIF" \* MERGEFORMATINET B． INCLUDEPICTURE "L26CGD7SX6A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6A.TIF" \* MERGEFORMATINET
C． INCLUDEPICTURE "L26CGD7SX6B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6B.TIF" \* MERGEFORMATINET D． INCLUDEPICTURE "L26CGD7SX6C.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX6C.TIF" \* MERGEFORMATINET
知识点三　同旁内角
3．图中的∠3和∠6虽然也都在直线AB，CD之间，但是它们在直线EF的同一旁(左侧)，具有这种位置关系的一对角叫作同旁内角．像这样的角还有∠4和∠5．
INCLUDEPICTURE "25SX-40-.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40-.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-40-.TIF" \* MERGEFORMATINET
练习3　(教材P7例3变式)如图，下列各角与∠B不是同旁内角的是(　B　).
INCLUDEPICTURE "L26CGD7SX7.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX7.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX7.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX7.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX7.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX7.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX7.TIF" \* MERGEFORMATINET
A．∠BAE B．∠BAD
C．∠C D．∠BAC
知识点四　熟练判断两个角的位置关系
练习4　(教材P7例3变式)如图，下列结论中错误的是(　B　).
INCLUDEPICTURE "25SX-48.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-48.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-48.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-48.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-48.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-48.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-48.TIF" \* MERGEFORMATINET
A．∠1与∠2是同旁内角
B．∠2与∠5是内错角
C．∠1与∠6是内错角
D．∠3与∠5是同位角
eq \o(\s\up7( INCLUDEPICTURE "课后练习.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET ),\s\do5(　　　　　　　))
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 基础巩固
1．如图，两只手的食指和拇指在同一平面内，它们构成的一对角可以看成是(　D　).
INCLUDEPICTURE "25SX-49A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-49A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-49A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-49A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-49A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-49A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-49A.TIF" \* MERGEFORMATINET
A．对顶角 B．同位角
C．内错角 D．同旁内角
2．如图，下列说法正确的是(　D　).
INCLUDEPICTURE "L26CGD7SX8.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX8.TIF" \* MERGEFORMATINET
A.∠1与∠2是同位角
B．∠1与∠3是同位角
C．∠2与∠3是内错角
D．∠2与∠3是同旁内角
3．如图，下列说法错误的是(　D　).
INCLUDEPICTURE "25SX-52.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-52.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-52.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-52.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-52.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-52.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-52.TIF" \* MERGEFORMATINET
A．∠3和∠B是同旁内角
B．∠A和∠C是同旁内角
C．∠2和∠3是内错角
D．∠1和∠3是同位角
4．下列各图中，∠1与∠2不是内错角的是(　C　).
A． INCLUDEPICTURE "25SX-51.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51.TIF" \* MERGEFORMATINET B． INCLUDEPICTURE "25SX-51A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51A.TIF" \* MERGEFORMATINET
C． INCLUDEPICTURE "25SX-51B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51B.TIF" \* MERGEFORMATINET D． INCLUDEPICTURE "25SX-51C.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-51C.TIF" \* MERGEFORMATINET
5．如图．
INCLUDEPICTURE "25SX-54.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-54.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-54.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-54.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-54.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-54.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-54.TIF" \* MERGEFORMATINET
(1)∠1与∠3是直线AB，AF被直线________所截构成的________角；
(2)∠2与∠4是直线________被直线BC所截构成的________角；
(3)图中∠5的同旁内角有________个，它们是________________；
(4)直线ED，BC被直线AB所截，则∠1与________是同位角；
(5)直线ED，BC被直线AF所截，则∠3与________是内错角．
【答案】(1)DE　内错
(2)AB，AF　同位
(3)3　∠A，∠3，∠2
(4)∠2
(5)∠4
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 能力达标
6．下列各图中，∠1与∠2是同位角的是(　A　).
A． INCLUDEPICTURE "25SX-55.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55.TIF" \* MERGEFORMATINET B． INCLUDEPICTURE "25SX-55A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55A.TIF" \* MERGEFORMATINET
C． INCLUDEPICTURE "25SX-55B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55B.TIF" \* MERGEFORMATINET D． INCLUDEPICTURE "25SX-55C.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-55C.TIF" \* MERGEFORMATINET
7．如图．
INCLUDEPICTURE "25SX-53.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-53.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-53.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-53.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-53.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-53.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-53.TIF" \* MERGEFORMATINET
(1)∠1与∠2是________角，它们是直线________被直线________所截而得到的角；
(2)∠3与∠4是直线____________被直线________所截而得到的角；
(3)直线AB，BE被直线AC所截而成的内错角是____________，同旁内角是____________；
(4)同位角共________对，内错角共________对，同旁内角共________对．
【答案】(1)内错　AD，BC　AC
(2)AB，CD　AC
(3)∠3与∠ACE　∠3与∠2
(4)4　6　12
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 挑战创新
8．如图，直线CD与∠AOB的边OB相交．
INCLUDEPICTURE "L26CGD7SX9.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX9.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX9.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX9.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX9.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX9.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX9.TIF" \* MERGEFORMATINET
(1)写出图中的同位角、内错角和同旁内角．
(2)如果∠1＝∠2，那么∠1与∠4相等吗？∠1与∠5互补吗？为什么？
【解】(1)∠1与∠4是同位角；∠1与∠2是内错角；∠1与∠5是同旁内角．
(2)如果∠1＝∠2，那么∠1与∠4相等，∠1与∠5互补. 理由如下：
因为∠1＝∠2，∠2＝∠4，
所以∠1＝∠4.
因为∠1＝∠2，∠2＋∠5＝180°，
所以∠1＋∠5＝180°.7．1.2　两条直线垂直
INCLUDEPICTURE "学习目标上.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET
1.理解垂线、垂线段的概念，能用三角板或量角器过一点画已知直线的垂线．2．掌握基本事实：同一平面内，过一点有且只有一条直线与已知直线垂直．3．了解垂线段最短的性质．4．理解点到直线的距离的意义，能度量点到直线的距离．
eq \o(\s\up7( INCLUDEPICTURE "知识梳理.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET ),\s\do5(　　　　　　　))
知识点一　垂直的定义
1．一般地，当两条直线a，b相交所成的四个角中，有一个角是直角时，我们说直线a与b互相垂直，其中的一条直线叫作另一条直线的垂线，它们的交点叫作垂足．若直线a与直线b互相垂直，记作a⊥b．
练习1　如图，直线AB，CD相交于点O，过点O作OE⊥OD，若∠AOD＝5∠AOC，则∠AOE的度数为(　B　).
INCLUDEPICTURE "25SX-23.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-23.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-23.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-23.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-23.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-23.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-23.TIF" \* MERGEFORMATINET
A．55° B．60°
C．65° D．70°
知识点二　垂线的画法
练习2　(教材P5探究变式)过点P作AB的垂线CD，下列选项中，三角尺的放法正确的是(　C　).
A． INCLUDEPICTURE "25SX-25.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25.TIF" \* MERGEFORMATINET B． INCLUDEPICTURE "25SX-25A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25A.TIF" \* MERGEFORMATINET
C． INCLUDEPICTURE "25SX-25B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25B.TIF" \* MERGEFORMATINET D． INCLUDEPICTURE "25SX-25C.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-25C.TIF" \* MERGEFORMATINET
知识点三　垂线、垂线段的性质
2．性质1(基本事实)：在同一平面内，过一点有且只有一条直线与已知直线垂直．
性质2：连接直线外一点与直线上各点的所有线段中，垂线段最短．简单说成：垂线段最短．
练习3　(教材P6探究变式)如图，直线l表示一段河道，点P表示水池，现要从河道l向水池P引水，设计了四条水渠开挖路线PA，PB，PC，PD，其中PB⊥l，要使挖渠的路线最短，可以选择的路线是(　B　).
INCLUDEPICTURE "L26CGD7SX4.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX4.TIF" \* MERGEFORMATINET
A．PA B．PB
C．PC D．PD
知识点四　点到直线的距离
3．直线外一点到这条直线的垂线段的长度，叫作点到直线的距离．
练习4　已知P为直线m外一点，A，B，C为直线m上三点，PA＝5 cm，PB＝6 cm，PC＝7 cm，则点P到直线m的距离(　D　).
A．等于6 cm
B．等于5 cm
C．小于5 cm
D．不大于5 cm
eq \o(\s\up7( INCLUDEPICTURE "课后练习.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET ),\s\do5(　　　　　　　))
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 基础巩固
1．如图，AC⊥BC，CD⊥AB，则点B到CD的距离是线段(　A　)的长度．
INCLUDEPICTURE "25SX-31.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-31.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-31.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-31.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-31.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-31.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-31.TIF" \* MERGEFORMATINET
A．BD B．BC
C．AD D．CD
2．如图，OC⊥AB，垂足为O，直线DE经过点O，∠COD＝52°，则∠BOE＝(　B　).
INCLUDEPICTURE "25SX-32.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-32.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-32.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-32.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-32.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-32.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-32.TIF" \* MERGEFORMATINET
A．28° B．38°
C．48° D．60°
3．如图，CA⊥BE于点A，AD⊥BF于点D，则下列说法正确的是(　B　).
INCLUDEPICTURE "25SX-33.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-33.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-33.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-33.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-33.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-33.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-33.TIF" \* MERGEFORMATINET
①∠α的余角只有∠B；②∠α的补角是∠DAE；③∠α与∠ACF互补；④∠α与∠DAC互余．
A．①②④ B．②③④
C．①④ D．②④
4．下列说法中，正确的个数是(　A　).
①对顶角相等；②一个角和另一个角两边分别垂直，则这两个角的度数相等；③过一点有且只有一条直线与已知直线垂直；④直线外一点到这条直线的垂线段叫作点到直线的距离．
A．1 B．2
C．3 D．4
5．如图，点A在点O的南偏东60°方向上，若OA⊥OB，则点B在点O的________方向上．
INCLUDEPICTURE "25SX-34.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-34.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-34.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-34.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-34.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-34.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-34.TIF" \* MERGEFORMATINET
【答案】南偏西30°(或西偏南60°)
6．如图，直线AB，CD相交于点O，∠MOB＝90°.
INCLUDEPICTURE "25SX-35.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-35.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-35.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-35.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-35.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-35.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-35.TIF" \* MERGEFORMATINET
(1)若∠1＝∠2，判断ON与CD的位置关系．请将下面的解题过程补充完整，在括号内填写理由．
解：ON________CD.理由如下：
因为OM⊥AB，
所以∠AOM＝________°，
所以________＋∠AOC＝90°.
又∠1＝∠2，
所以________＋∠AOC＝90°(等量代换)，
即∠CON＝90°，
所以__________(________________).
(2)若∠BOC＝4∠1，求∠MOD的度数．
【解】(1)⊥　90　∠1　∠2　ON⊥CD　垂直的定义
(2)因为OM⊥AB，
所以∠BOM＝90°.
因为∠BOC＝∠1＋∠BOM，
所以∠1＋90°＝4∠1，
所以∠1＝30°，
所以∠AOC＝90°－∠1＝90°－30°＝60°，
所以∠BOD＝∠AOC＝60°，
所以∠MOD＝∠MOB＋∠BOD＝90°＋60°＝150°.
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 能力达标
7．如图，E是直线CA上一点，∠FEA＝40°，射线EB平分∠CEF，GE⊥EF，则∠GEB＝(　B　).
INCLUDEPICTURE "K84.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\K84.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\K84.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\K84.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\K84.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\K84.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\K84.TIF" \* MERGEFORMATINET
A．10° B．20°
C．30° D．40°
8．在直线AB上任取一点O，过点O作射线OC，OD，使OC⊥OD，当∠AOC＝28°时，∠BOD的度数是________．
【答案】62°或118°
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 挑战创新
9．如图，已知直线AB，CD相交于点O，OE，OF为射线，OE⊥AB，OF平分∠BOC.
INCLUDEPICTURE "L26CGD7SX5.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX5.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX5.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX5.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX5.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX5.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX5.TIF" \* MERGEFORMATINET
(1)若∠EOF＝30°，求∠BOD的度数．
(2)试问∠EOF和∠BOD有什么数量关系？请说明理由．
【解】(1)因为OE⊥AB，
所以∠AOE＝90°，∠EOB＝90°.
因为∠EOF＝30°，
所以∠FOB＝∠EOB－∠EOF＝60°.
因为OF平分∠BOC，
所以∠BOC＝2∠FOB＝120°，
所以∠BOD＝180°－∠BOC＝60°.
(2)∠BOD＝2∠EOF.理由如下：
设∠EOF＝x.
因为OE⊥AB，所以∠AOE＝90°，
所以∠EOB＝90°.
因为∠EOF＝x，
所以∠FOB＝∠EOB－∠EOF＝90°－x.
因为OF平分∠BOC，
所以∠BOC＝2∠FOB＝180°－2x，
所以∠BOD＝180°－∠BOC＝180°－(180°－2x)＝2x，
所以∠BOD＝2∠EOF.7．1.2　两条直线垂直
1.理解垂线、垂线段的概念，能用三角板或量角器过一点画已知直线的垂线．2．掌握基本事实：同一平面内，过一点有且只有一条直线与已知直线垂直．3．了解垂线段最短的性质．4．理解点到直线的距离的意义，能度量点到直线的距离．
eq \o(\s\up7(),\s\do5(　　　　　　　))
知识点一　垂直的定义
1．一般地，当两条直线a，b相交所成的四个角中，有一个角是 时，我们说直线a与b ，其中的一条直线叫作另一条直线的 ，它们的交点叫作 ．若直线a与直线b互相垂直，记作 ．
练习1　如图，直线AB，CD相交于点O，过点O作OE⊥OD，若∠AOD＝5∠AOC，则∠AOE的度数为(　　).
A．55° B．60°
C．65° D．70°
知识点二　垂线的画法
练习2　(教材P5探究变式)过点P作AB的垂线CD，下列选项中，三角尺的放法正确的是(　　).
A． B．
C． D．
知识点三　垂线、垂线段的性质
2．性质1(基本事实)：在同一平面内，过一点 条直线与已知直线垂直．
性质2：连接 一点与直线上各点的所有线段中， 最短．简单说成： 最短．
练习3　(教材P6探究变式)如图，直线l表示一段河道，点P表示水池，现要从河道l向水池P引水，设计了四条水渠开挖路线PA，PB，PC，PD，其中PB⊥l，要使挖渠的路线最短，可以选择的路线是(　　).
A．PA B．PB
C．PC D．PD
知识点四　点到直线的距离
3．直线外一点到这条直线的垂线段的 ，叫作点到直线的距离．
练习4　已知P为直线m外一点，A，B，C为直线m上三点，PA＝5 cm，PB＝6 cm，PC＝7 cm，则点P到直线m的距离(　　).
A．等于6 cm
B．等于5 cm
C．小于5 cm
D．不大于5 cm
eq \o(\s\up7(),\s\do5(　　　　　　　))
基础巩固
1．如图，AC⊥BC，CD⊥AB，则点B到CD的距离是线段(　　)的长度．
A．BD B．BC
C．AD D．CD
2．如图，OC⊥AB，垂足为O，直线DE经过点O，∠COD＝52°，则∠BOE＝(　　).
A．28° B．38°
C．48° D．60°
3．如图，CA⊥BE于点A，AD⊥BF于点D，则下列说法正确的是(　　).
①∠α的余角只有∠B；②∠α的补角是∠DAE；③∠α与∠ACF互补；④∠α与∠DAC互余．
A．①②④ B．②③④
C．①④ D．②④
4．下列说法中，正确的个数是(　　).
①对顶角相等；②一个角和另一个角两边分别垂直，则这两个角的度数相等；③过一点有且只有一条直线与已知直线垂直；④直线外一点到这条直线的垂线段叫作点到直线的距离．
A．1 B．2
C．3 D．4
5．如图，点A在点O的南偏东60°方向上，若OA⊥OB，则点B在点O的________方向上．
6．如图，直线AB，CD相交于点O，∠MOB＝90°.
(1)若∠1＝∠2，判断ON与CD的位置关系．请将下面的解题过程补充完整，在括号内填写理由．
解：ON________CD.理由如下：
因为OM⊥AB，
所以∠AOM＝________°，
所以________＋∠AOC＝90°.
又∠1＝∠2，
所以________＋∠AOC＝90°(等量代换)，
即∠CON＝90°，
所以__________(________________).
(2)若∠BOC＝4∠1，求∠MOD的度数．
能力达标
7．如图，E是直线CA上一点，∠FEA＝40°，射线EB平分∠CEF，GE⊥EF，则∠GEB＝(　　).
A．10° B．20°
C．30° D．40°
8．在直线AB上任取一点O，过点O作射线OC，OD，使OC⊥OD，当∠AOC＝28°时，∠BOD的度数是________．
挑战创新
9．如图，已知直线AB，CD相交于点O，OE，OF为射线，OE⊥AB，OF平分∠BOC.
(1)若∠EOF＝30°，求∠BOD的度数．
(2)试问∠EOF和∠BOD有什么数量关系？请说明理由．7．1.1　两条直线相交
INCLUDEPICTURE "学习目标上.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\学习目标上.TIF" \* MERGEFORMATINET
1.理解对顶角、邻补角的概念．2．探索并掌握对顶角相等的性质．3．通过在图形中辨认对顶角、邻补角，培养学生的识图能力．
INCLUDEPICTURE "知识梳理.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\知识梳理.TIF" \* MERGEFORMATINET
知识点一　邻补角的概念
1．如图，∠AOC和∠AOD有一条公共边，它们的另一边互为反向延长线(∠AOC和∠AOD互补)，具有这种位置关系的两个角，互为邻补角．
INCLUDEPICTURE "25SX-2.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2.TIF" \* MERGEFORMATINET
练习1　(教材P2探究变式)在下列各图中，∠1和∠2互为邻补角的是(　B　).
A． INCLUDEPICTURE "25SX-4.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4.TIF" \* MERGEFORMATINET B． INCLUDEPICTURE "25SX-4A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4A.TIF" \* MERGEFORMATINET
C． INCLUDEPICTURE "25SX-4B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4B.TIF" \* MERGEFORMATINET D． INCLUDEPICTURE "25SX-4C.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-4C.TIF" \* MERGEFORMATINET
知识点二　对顶角的概念及性质
2．(1)如图，∠AOC和∠BOD有一个公共顶点，并且∠AOC的两边分别是∠BOD的两边的反向延长线，具有这种位置关系的两个角，互为对顶角．
(2)互为对顶角的两个角相等，即对顶角相等．
INCLUDEPICTURE "25SX-2+.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2+.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-2+.TIF" \* MERGEFORMATINET
练习2　(教材P2探究变式)在下列各图中，∠1和∠2互为对顶角的是(　B　).
A． INCLUDEPICTURE "25SX-6.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6.TIF" \* MERGEFORMATINET B． INCLUDEPICTURE "25SX-6A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6A.TIF" \* MERGEFORMATINET
C． INCLUDEPICTURE "25SX-6B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6B.TIF" \* MERGEFORMATINET D． INCLUDEPICTURE "25SX-6C.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-6C.TIF" \* MERGEFORMATINET
知识点三　运用邻补角、对顶角的性质进行角度的计算
练习3　(教材P3例1变式)如图，直线AB，CD相交于点O，∠AOC ＝ 85°，OE把∠BOD分成两部分，且∠BOE∶∠DOE＝2∶3，求∠AOE的度数．
INCLUDEPICTURE "25SX-8.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-8.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-8.TIF" \* MERGEFORMATINET
【解】因为∠AOC＝85°，
∠AOC＝∠BOD，
所以∠BOD＝85°.
由∠BOE∶∠DOE＝2∶3，
设∠BOE＝2x，∠DOE＝3x.
又因为∠BOD＝∠BOE＋∠DOE，
所以2x＋3x＝85°，
解得x＝17°，
所以∠DOE＝51°.
因为∠AOC＋∠AOD＝180°，
所以∠AOD＝180°－∠AOC＝180°－85°＝95°，
所以∠AOE＝∠AOD＋∠DOE＝95°＋51°＝146°.
知识点四　利用邻补角、对顶角的性质解决实际问题
练习4　为测量古塔的墙底角∠AOB的度数，小颖、小明两人的测量方案见下表：
小颖的方案 小明的方案
INCLUDEPICTURE "25SX-10.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-10.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-10.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-10.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-10.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-10.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-10.TIF" \* MERGEFORMATINET INCLUDEPICTURE "25SX-11.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-11.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-11.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-11.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-11.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-11.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-11.TIF" \* MERGEFORMATINET
分别作AO，BO的延长线OC，OD，量出∠COD的度数，就得到∠AOB的度数． 作BO的延长线OD，量出∠AOD的度数后可通过180°－∠AOD得到∠AOB的度数．
下列判断正确的是(　C　).
A．小颖能得到∠AOB的度数，小明不能
B．小明能得到∠AOB的度数，小颖不能
C．两人都能得到∠AOB的度数
D．两人都不能得到∠AOB的度数
eq \o(\s\up7( INCLUDEPICTURE "课后练习.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\课后练习.TIF" \* MERGEFORMATINET ),\s\do5(　　　　　　　))
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 基础巩固
1．下列各图中，∠1和∠2互为对顶角的有(　B　).
　 eq \o(\s\up7( INCLUDEPICTURE "25SX-14.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14.TIF" \* MERGEFORMATINET ),\s\do5(①))　　　　 eq \o(\s\up7( INCLUDEPICTURE "25SX-14A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14A.TIF" \* MERGEFORMATINET ),\s\do5(②))　　
eq \o(\s\up7( INCLUDEPICTURE "25SX-14B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14B.TIF" \* MERGEFORMATINET ),\s\do5(③))　　　　 eq \o(\s\up7( INCLUDEPICTURE "25SX-14C.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14C.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-14C.TIF" \* MERGEFORMATINET ),\s\do5(④))
A．0个　　　　　 B．1个
C．2个 D．3个
2．如图，直线AB，CD相交于点O，OE平分∠BOD，若∠AOC＝40°，则∠COE的度数为(　D　).
INCLUDEPICTURE "25SX-15.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-15.TIF" \* MERGEFORMATINET
A．145° B．150°
C．155° D．160°
3．已知∠1与∠2互为对顶角，∠2与∠3互余，若∠3＝50°，则∠1的度数是(　A　).
A．40° B．90°
C．135° D．40°或140°
4．如图，在灯塔O处观测到轮船A在北偏西66°方向上，轮船B在OA的反向延长线上，轮船C在灯塔O的东南方向上，则∠BOC的度数为(　D　).
INCLUDEPICTURE "L26CGD7SX2.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX2.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX2.TIF" \* MERGEFORMATINET
A.45° B．31°
C．24° D．21°
5．如图，晓丹家有一个破损的扇形零件，晓丹利用图中的量角器量出这个扇形零件的圆心角的度数，那么这个破损扇形零件的圆心角的度数是________．
INCLUDEPICTURE "25SX-17.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-17.TIF" \* MERGEFORMATINET
【答案】30°
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 能力达标
6．如图，直线AB，CD相交于点O，OE平分∠BOD，OF平分∠COE，且∠1∶∠2＝1∶4，则∠COF的度数为________．
INCLUDEPICTURE "25SX-19.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-19.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-19.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-19.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-19.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-19.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-19.TIF" \* MERGEFORMATINET
【答案】75°
7．如图，直线AB与CD相交于点O，OC平分∠AOM，且∠AOM＝90°，射线ON在∠BOM内部．
INCLUDEPICTURE "L26CGD7SX3.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX3.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX3.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX3.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX3.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX3.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX3.TIF" \* MERGEFORMATINET
(1)求∠AOD的度数；
(2)若∠BOC＝5∠NOB，求∠MON的度数．
【解】(1)因为∠AOM＝90°，OC平分∠AOM，
所以∠AOC＝∠AOM＝×90°＝45°.
因为∠AOC＋∠AOD＝180°，
所以∠AOD＝180°－∠AOC＝180°－45°＝135°.
(2)因为∠BOC＝∠AOD＝135°，
∠BOC＝5∠NOB，
所以∠NOB＝27°.
因为∠AOM＝90°，
所以∠BOM＝90°，
所以∠MON＝∠BOM－∠NOB＝90°－27°＝63°.
INCLUDEPICTURE "三角.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\三角.TIF" \* MERGEFORMATINET 挑战创新
8．(跨学科融合)将一根木棒放入盛有水的玻璃杯中，一头露出水面，一头浸入水中，我们可以发现浸入水中的部分“变弯了”．它真的变弯了吗？ 其实没有，这只是光的折射现象，即光从空气斜射入水中，光线的传播方向发生改变．如图，假设一束光AO射入水中，在水中的传播路径为OB，∠1与∠2互为对顶角吗？如果不互为对顶角，如何比较它们的大小？
INCLUDEPICTURE "25SX-20.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20.TIF" \* MERGEFORMATINET
【解】∠1与∠2不互为对顶角．
如图，延长AO，可得∠2>∠1.
INCLUDEPICTURE "25SX-20A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-20A.TIF" \* MERGEFORMATINET

展开更多......

收起↑