资源简介

7．2.2　平行线的判定
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.经历探索两直线平行条件的过程，理解两直线平行的条件，会运用条件判定两直线平行．2．掌握平行线基本事实Ⅱ：两条直线被第三条直线所截，如果同位角相等，那么这两条直线平行．3．探索并证明平行线的判定定理：两条直线被第三条直线所截，如果内错角相等(或同旁内角互补)，那么这两条直线平行．4．进一步掌握两直线平行的条件，并能解决一些简单的问题．5．初步了解推理论证的方法，会正确地书写简单的推理过程．
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　平行线的判定方法
1．两条直线被第三条直线所截，如果同位角相等，那么这两条直线平行．简单说成：同位角相等，两直线平行．
2．两条直线被第三条直线所截，如果内错角相等，那么这两条直线平行．简单说成：内错角相等，两直线平行．
3．两条直线被第三条直线所截，如果同旁内角互补，那么这两条直线平行．简单说成：同旁内角互补，两直线平行．
练习1　如图，点E在BC的延长线上，下列条件中，不能推断AB∥CD的是(　B　).
INCLUDEPICTURE "25SX-71.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-71.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-71.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-71.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-71.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-71.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-71.TIF" \* MERGEFORMATINET
A．∠1＝∠2
B．∠3＝∠4
C．∠B＝∠5
D．∠B＋∠BCD＝180°
知识点二　添加条件，判定平行
练习2　如图，点E是AD延长线上一点，如果添加一个条件，使BC∥AD，则可添加的条件为(　A　).
INCLUDEPICTURE "L26CGD7SX14.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX14.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX14.TIF" \* MERGEFORMATINET
A．∠C＋∠ADC＝180°
B．∠A＋∠ABD＝180°
C．∠CBD＝∠ADC
D．∠C＝∠CDA
知识点三　平行线判定的实际应用
练习3　一辆汽车在公路上行驶，两次拐弯后，仍在原来的方向上行驶，那么两次拐弯的方向可能是(　D　).
A．先右转50°，后左转40°
B．先右转50°，后左转130°
C．先右转50°，后右转40°
D．先右转50°，后左转50°
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．已知a，b，c是直线，下列说法正确的是(　D　).
A．若a⊥b，b∥c，则a∥c
B．若a⊥b，b⊥c，则a⊥c
C．若a∥b，b⊥c，则a∥c
D．若a∥b，b∥c，则a∥c
2．如图，小明在地图上量得∠1＝∠2，由此判断幸福大街与平安大街互相平行，他判断的依据是(　B　).
INCLUDEPICTURE "25SX-83.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-83.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-83.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-83.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-83.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-83.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-83.TIF" \* MERGEFORMATINET
A．同位角相等，两直线平行
B．内错角相等，两直线平行
C．同旁内角互补，两直线平行
D．对顶角相等
3．如图，把三角尺的直角顶点放在直线b上．若∠1＝50°，则当∠2＝________时，a∥b.
INCLUDEPICTURE "L26CGD7SX15.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX15.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX15.TIF" \* MERGEFORMATINET
【答案】40°
4．如图，已知∠ABC＝∠ADC，BF，DE分别平分∠ABC与∠ADC，且∠1＝∠3.试说明：AB∥DC.(请根据条件进行推理，得出结论，并在括号内注明理由)
INCLUDEPICTURE "L26CGD7SX16.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX16.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX16.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX16.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX16.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX16.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX16.TIF" \* MERGEFORMATINET
解：因为BF，DE分别平分∠ABC与∠ADC(已知)，
所以∠1＝∠ABC，
∠2＝∠ADC(__________________).
因为∠ABC＝∠ADC(____________)，
所以∠____________＝∠____________(等量代换).
因为∠1＝∠3(____________)，
所以∠2＝∠__________(__________).
所以____________∥____________(__________________________).
【答案】角平分线的定义　已知　1　2　已知　3　等量代换　AB　DC　内错角相等，两直线平行
5．如图，已知三角形ABC中，∠ACB＝80°，点E，F分别在AB，AC上，ED交AC于点G，交BC的延长线于点D，∠FEG＝32°，∠CGD＝48°.试猜想EF与BC的位置关系，并说明理由．
INCLUDEPICTURE "L26CGD7SX17.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX17.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX17.TIF" \* MERGEFORMATINET
【解】EF∥BC.理由如下：
因为∠CGD＝48°，
所以∠EGF＝∠CGD＝48°.
因为∠FEG＝32°，
所以∠GFE＝180°－∠EGF－∠FEG＝180°－48°－32°＝100°.
因为∠ACB＝80°，
所以∠GFE＋∠ACB＝180°，
所以EF∥BC.
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，在下列四组条件：①∠1＝∠2，②∠3＝∠4，③∠BAD＋∠ABC＝180°，④∠BAD＋∠ADC＝180°中，能判定AD∥BC的是________(填序号).
INCLUDEPICTURE "25SX-81.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-81.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-81.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-81.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-81.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-81.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-81.TIF" \* MERGEFORMATINET
【答案】①②③
7．如图，已知点O在直线AB上，射线OD平分∠BOC，过点O作OE⊥OD，G是射线OB上一点，连接DG，满足∠ODG＋∠DOG＝90°.
INCLUDEPICTURE "L26CGD7SX18.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX18.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX18.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX18.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX18.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX18.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\L26CGD7SX18.TIF" \* MERGEFORMATINET
(1)试说明：∠AOE＝∠ODG；
(2)若∠ODG＝∠C，请说明：CD∥OE.
【解】(1)因为OE⊥OD，
所以∠DOE＝90°.
因为∠DOE＋∠AOE＋∠DOG＝180°，
所以∠AOE＋∠DOG＝90°.
因为∠ODG＋∠DOG＝90°，
所以∠AOE＝∠ODG.
(2)因为OD平分∠BOC，
所以∠DOG＝∠COD＝∠BOC.
因为OE⊥OD，所以∠DOE＝90°，
所以∠COE＋∠COD＝90°.
因为∠ODG＋∠DOG＝90°，
所以∠ODG＝∠COE.
因为∠ODG＝∠C，
所以∠C＝∠COE，
所以CD∥OE.
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．实践探究题
【学习新知】射到平面镜上的光线(入射光线)和反射后的光线(反射光线)与平面镜所夹的角相等．如图1，若入射光线与水平镜面夹角为∠1，反射光线与水平镜面夹角为∠2，则∠1＝∠2.
eq \o(\s\up7( INCLUDEPICTURE "25SX-86.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86.TIF" \* MERGEFORMATINET ),\s\do5(图1))　 eq \o(\s\up7( INCLUDEPICTURE "25SX-86A.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86A.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86A.TIF" \* MERGEFORMATINET ),\s\do5(图2))
eq \o(\s\up7( INCLUDEPICTURE "25SX-86B.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86B.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-86B.TIF" \* MERGEFORMATINET ),\s\do5(图3))
(1)【初步应用】如图2，有两块平面镜AB，BC，入射光线DO1经过两次反射，得到反射光线O2E，若∠B＝90°，说明：DO1∥O2E；
(2)【拓展探究】如图3，有三块平面镜AB，BC，CD，入射光线EO1经过三次反射，得到反射光线O3F，已知∠1＝36°，∠B＝120°，若要使EO1∥O3F，则∠C为多少度？
【解】(1)因为∠B＝90°，∠B＋∠2＋∠3＝180°，所以∠2＋∠3＝90°.
由题意知∠1＝∠2，∠3＝∠4，
所以∠1＋∠2＋∠3＋∠4＝180°.
又因为∠1＋∠DO1O2＋∠2＝180°，
∠3＋∠O1O2E＋∠4＝180°，
所以∠DO1O2＋∠O1O2E＝180°，
所以DO1∥O2E.
(2)如图，过点O2作O2M∥EO1.
INCLUDEPICTURE "25SX-87.TIF" INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-87.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-87.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-87.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-87.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-87.TIF" \* MERGEFORMATINET INCLUDEPICTURE "C:\\Users\\Administrator\\AppData\\Local\\Microsoft\\Windows\\INetCache\\Content.Word\\25SX-87.TIF" \* MERGEFORMATINET
因为∠1＝36°，∠B＝120°，∠1＝∠2，
所以∠2＝∠1＝36°，
所以∠3＝180°－∠B－∠2＝180°－120°－36°＝24°，∠EO1O2＝180°－∠1－∠2＝180°－36°－36°＝108°.
又∠3＝∠4，
所以∠4＝∠3＝24°，
所以∠O1O2O3＝180°－∠3－∠4＝180°－24°－24°＝132°.
因为O2M∥O1E，
所以∠O1O2M＝180°－∠EO1O2＝180°－108°＝72°，
所以∠MO2O3＝∠O1O2O3－∠O1O2M＝132°－72°＝60°.
因为O2M∥EO1，EO1∥O3F，
所以O2M∥O3F，
所以∠O2O3F＝180°－∠MO2O3＝180°－60°＝120°.
又∠5＝∠6，
所以∠5＝∠6＝×(180°－∠O2O3F)＝×(180°－120°)＝30°，
所以∠C＝180°－∠4－∠5＝180°－24°－30°＝126°.7．2.2　平行线的判定
1.经历探索两直线平行条件的过程，理解两直线平行的条件，会运用条件判定两直线平行．2．掌握平行线基本事实Ⅱ：两条直线被第三条直线所截，如果同位角相等，那么这两条直线平行．3．探索并证明平行线的判定定理：两条直线被第三条直线所截，如果内错角相等(或同旁内角互补)，那么这两条直线平行．4．进一步掌握两直线平行的条件，并能解决一些简单的问题．5．初步了解推理论证的方法，会正确地书写简单的推理过程．
eq \o(\s\up7(),\s\do5(　　　　　　　))
知识点一　平行线的判定方法
1．两条直线被第三条直线所截，如果同位角相等，那么这两条直线平行．简单说成： ．
2．两条直线被第三条直线所截，如果内错角相等，那么这两条直线平行．简单说成： ．
3．两条直线被第三条直线所截，如果同旁内角互补，那么这两条直线平行．简单说成： ．
练习1　如图，点E在BC的延长线上，下列条件中，不能推断AB∥CD的是( ).
A．∠1＝∠2
B．∠3＝∠4
C．∠B＝∠5
D．∠B＋∠BCD＝180°
知识点二　添加条件，判定平行
练习2　如图，点E是AD延长线上一点，如果添加一个条件，使BC∥AD，则可添加的条件为( ).
A．∠C＋∠ADC＝180°
B．∠A＋∠ABD＝180°
C．∠CBD＝∠ADC
D．∠C＝∠CDA
知识点三　平行线判定的实际应用
练习3　一辆汽车在公路上行驶，两次拐弯后，仍在原来的方向上行驶，那么两次拐弯的方向可能是( ).
A．先右转50°，后左转40°
B．先右转50°，后左转130°
C．先右转50°，后右转40°
D．先右转50°，后左转50°
eq \o(\s\up7(),\s\do5(　　　　　　　))
基础巩固
1．已知a，b，c是直线，下列说法正确的是( ).
A．若a⊥b，b∥c，则a∥c
B．若a⊥b，b⊥c，则a⊥c
C．若a∥b，b⊥c，则a∥c
D．若a∥b，b∥c，则a∥c
2．如图，小明在地图上量得∠1＝∠2，由此判断幸福大街与平安大街互相平行，他判断的依据是( ).
A．同位角相等，两直线平行
B．内错角相等，两直线平行
C．同旁内角互补，两直线平行
D．对顶角相等
3．如图，把三角尺的直角顶点放在直线b上．若∠1＝50°，则当∠2＝________时，a∥b.
4．如图，已知∠ABC＝∠ADC，BF，DE分别平分∠ABC与∠ADC，且∠1＝∠3.试说明：AB∥DC.(请根据条件进行推理，得出结论，并在括号内注明理由)
解：因为BF，DE分别平分∠ABC与∠ADC(已知)，
所以∠1＝∠ABC，
∠2＝∠ADC(__________________).
因为∠ABC＝∠ADC(____________)，
所以∠____________＝∠____________(等量代换).
因为∠1＝∠3(____________)，
所以∠2＝∠__________(__________).
所以____________∥____________(__________________________).
5．如图，已知三角形ABC中，∠ACB＝80°，点E，F分别在AB，AC上，ED交AC于点G，交BC的延长线于点D，∠FEG＝32°，∠CGD＝48°.试猜想EF与BC的位置关系，并说明理由．
6．如图，在下列四组条件：①∠1＝∠2，②∠3＝∠4，③∠BAD＋∠ABC＝180°，④∠BAD＋∠ADC＝180°中，能判定AD∥BC的是________(填序号).
7．如图，已知点O在直线AB上，射线OD平分∠BOC，过点O作OE⊥OD，G是射线OB上一点，连接DG，满足∠ODG＋∠DOG＝90°.
(1)试说明：∠AOE＝∠ODG；
(2)若∠ODG＝∠C，请说明：CD∥OE.
8．实践探究题
【学习新知】射到平面镜上的光线(入射光线)和反射后的光线(反射光线)与平面镜所夹的角相等．如图1，若入射光线与水平镜面夹角为∠1，反射光线与水平镜面夹角为∠2，则∠1＝∠2.
eq \o(\s\up7(),\s\do5(图1))　 eq \o(\s\up7(),\s\do5(图2))
eq \o(\s\up7(),\s\do5(图3))
(1)【初步应用】如图2，有两块平面镜AB，BC，入射光线DO1经过两次反射，得到反射光线O2E，若∠B＝90°，说明：DO1∥O2E；
(2)【拓展探究】如图3，有三块平面镜AB，BC，CD，入射光线EO1经过三次反射，得到反射光线O3F，已知∠1＝36°，∠B＝120°，若要使EO1∥O3F，则∠C为多少度？

展开更多......

收起↑