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INCLUDEPICTURE "第六章章头.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/第六章章头.tif" \* MERGEFORMAT INCLUDEPICTURE "../../第六章章头.tif" \* MERGEFORMAT INCLUDEPICTURE "../../第六章章头.tif" \* MERGEFORMAT INCLUDEPICTURE "../第六章章头.tif" \* MERGEFORMAT
INCLUDEPICTURE "节.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/节.tif" \* MERGEFORMAT INCLUDEPICTURE "../../节.tif" \* MERGEFORMAT INCLUDEPICTURE "../../节.tif" \* MERGEFORMAT INCLUDEPICTURE "../节.tif" \* MERGEFORMAT INCLUDEPICTURE "节.tif" \* MERGEFORMAT
6.1　几何图形
6．1.1　立体图形与平面图形
eq \o(\s\up7( INCLUDEPICTURE "知识梳理.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "知识梳理.tif" \* MERGEFORMAT ),\s\do5(　　　　　　　))
知识点一　认识立体图形
1．有些几何图形(如长方体、正方体、圆柱、圆锥、球等)的各部分不都在同一平面内，它们是立体图形．
练习1　如图所示，陀螺是由几何体(　B　)组合而成的．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX109.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX109.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX109.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX109.tif" \* MERGEFORMAT INCLUDEPICTURE "SX109.tif" \* MERGEFORMAT
A．圆和三角形
B．圆柱和圆锥
C．长方体和圆锥
D．长方形和三角形
总结　从各种物体抽象出的几何图形，不考虑它们的颜色、质量和材质，只关注它们的形状、大小和位置关系．
知识点二　认识平面图形
2．有些几何图形(如线段、角、三角形、长方形、圆等)的各部分都在同一平面内，它们是平面图形．
练习2　下面的四个几何图形中，表示平面图形的是(　B　).
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX110.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX110.tif" \* MERGEFORMAT INCLUDEPICTURE "SX110.tif" \* MERGEFORMAT ),\s\do5(A)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX110a.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110a.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110a.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX110a.tif" \* MERGEFORMAT INCLUDEPICTURE "SX110a.tif" \* MERGEFORMAT ),\s\do5(B)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX110b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110b.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX110b.tif" \* MERGEFORMAT INCLUDEPICTURE "SX110b.tif" \* MERGEFORMAT ),\s\do5(C)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX110c.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110c.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX110c.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX110c.tif" \* MERGEFORMAT INCLUDEPICTURE "SX110c.tif" \* MERGEFORMAT ),\s\do5(D))
总结　平面图形是由在同一平面内的点和线(直线或曲线)组成的图形．如直线、射线、线段、角、三角形、长方形、平行四边形、梯形、圆等．
知识点三　从不同方向看立体图形
练习3　从左面观察如图所示的几何体，得到的平面图形是(　D　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX111.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX111.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX111.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX111.tif" \* MERGEFORMAT INCLUDEPICTURE "SX111.tif" \* MERGEFORMAT
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX112.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX112.tif" \* MERGEFORMAT INCLUDEPICTURE "SX112.tif" \* MERGEFORMAT ),\s\do5(A)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX112A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX112A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX112A.tif" \* MERGEFORMAT ),\s\do5(B)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX112b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112b.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112b.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX112b.tif" \* MERGEFORMAT INCLUDEPICTURE "SX112b.tif" \* MERGEFORMAT ),\s\do5(C)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX112C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX112C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX112C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX112C.tif" \* MERGEFORMAT ),\s\do5(D))
总结　从不同方向看立体图形
知识点四　立体图形的展开图
3．有些立体图形是由一些平面图形围成的，将它们的表面适当展开，可以展开成平面图形．这样的平面图形称为相应立体图形的展开图．
练习4　下面的平面展开图与图下方的立体图形名称不相符的是(　C　).
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX115.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX115.tif" \* MERGEFORMAT INCLUDEPICTURE "SX115.tif" \* MERGEFORMAT ),\s\do5(A.正方体)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX115A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX115A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX115A.tif" \* MERGEFORMAT ),\s\do5(B.长方体))
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX115B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115B.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX115B.tif" \* MERGEFORMAT INCLUDEPICTURE "SX115B.tif" \* MERGEFORMAT ),\s\do5(C.三棱锥　)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX115C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX115C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX115C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX115C.tif" \* MERGEFORMAT ),\s\do5(D.圆柱体))
【解析】选项C中的图形折叠后成为三棱柱，不是三棱锥，因此选项C符合题意．故选C.
总结　由立体图形展开图可以识别立体图形的形状，展开图中有圆形，一般考虑圆柱或圆锥；展开图中有三角形，一般考虑棱柱或棱锥；展开图中只有长方形或正方形，一般考虑长方体或正方体；展开图中有扇形，一般考虑圆锥．
eq \o(\s\up7( INCLUDEPICTURE "课后练习.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "课后练习.tif" \* MERGEFORMAT ),\s\do5(　　　　　　　))
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 基础巩固
1．下面几何体中，是圆柱的为(　C　).
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX117.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX117.tif" \* MERGEFORMAT INCLUDEPICTURE "SX117.tif" \* MERGEFORMAT ),\s\do5(A)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX117A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX117A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX117A.tif" \* MERGEFORMAT ),\s\do5(B)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX117B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117B.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX117B.tif" \* MERGEFORMAT INCLUDEPICTURE "SX117B.tif" \* MERGEFORMAT ),\s\do5(C)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX117C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX117C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX117C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX117C.tif" \* MERGEFORMAT ),\s\do5(D))
2．下列图形是棱锥侧面展开图的是(　D　).
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX118.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX118.tif" \* MERGEFORMAT INCLUDEPICTURE "SX118.tif" \* MERGEFORMAT ),\s\do5(A)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX118A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX118A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX118A.tif" \* MERGEFORMAT ),\s\do5(B)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX118B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118B.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX118B.tif" \* MERGEFORMAT INCLUDEPICTURE "SX118B.tif" \* MERGEFORMAT ),\s\do5(C)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX118C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX118C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX118C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX118C.tif" \* MERGEFORMAT ),\s\do5(D))
3．如图所示的六角螺母，从上面看，得到的图形是(　B　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX119.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX119.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX119.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX119.tif" \* MERGEFORMAT INCLUDEPICTURE "SX119.tif" \* MERGEFORMAT
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX120.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX120.tif" \* MERGEFORMAT INCLUDEPICTURE "SX120.tif" \* MERGEFORMAT ),\s\do5(A)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX120A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX120A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX120A.tif" \* MERGEFORMAT ),\s\do5(B)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX120B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120B.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX120B.tif" \* MERGEFORMAT INCLUDEPICTURE "SX120B.tif" \* MERGEFORMAT ),\s\do5(C)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX120C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX120C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX120C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX120C.tif" \* MERGEFORMAT ),\s\do5(D))
4．下图是一正方体的表面展开图．将其折叠成正方体后，与顶点K距离最远的顶点是(　D　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX121.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX121.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX121.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX121.tif" \* MERGEFORMAT INCLUDEPICTURE "SX121.tif" \* MERGEFORMAT
A．A点 B．B点
C．C点 D．D点
【解析】把展开图折叠成正方体后如图所示：
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX291.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX291.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX291.TIF" \* MERGEFORMAT INCLUDEPICTURE "../SX291.TIF" \* MERGEFORMAT INCLUDEPICTURE "SX291.TIF" \* MERGEFORMAT
所以与顶点K距离最远的顶点是D点，故选D.
5．用棱长相同的小正方体摆成如图所示的几何体，第1层有1个正方体，第2层有3个正方体，第3层有6个正方体，按图中摆放的方法类推，第20层有________个正方体．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX124.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX124.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX124.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX124.tif" \* MERGEFORMAT INCLUDEPICTURE "SX124.tif" \* MERGEFORMAT
【答案】210
【解析】第1层的正方体有1个，
第2层的正方体有1＋2＝3(个)，
第3层的正方体有1＋2＋3＝6(个)，
第4层的正方体有1＋2＋3＋4＝10(个)，
……
第20层的正方体有1＋2＋3＋4＋…＋19＋20＝210(个).
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 能力达标
6．如图所示，在一个正方体展开图六个面上依次书写“明”“天”“开”“心”“幸”“福”，则折叠后与“明”相对的是(　C　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX125.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX125.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX125.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX125.tif" \* MERGEFORMAT INCLUDEPICTURE "SX125.tif" \* MERGEFORMAT
A．心 B．幸
C．福 D．天
7．下列四个几何体中，从上面看与从左面看的图形相同的几何体有(　B　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX328.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX328.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX328.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX328.tif" \* MERGEFORMAT INCLUDEPICTURE "SX328.tif" \* MERGEFORMAT
A．1个 B．2个
C．3个 D．4个
8．下图是一个长方体墨水瓶纸盒的表面展开图，已知纸盒中相对两个面上的数互为相反数．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX126.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX126.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX126.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX126.tif" \* MERGEFORMAT INCLUDEPICTURE "SX126.tif" \* MERGEFORMAT
(1)填空：a＝________，b＝________，c＝________；
(2)求(a＋b)c－(b＋c)a＋的值．
(1)【答案】0　2　－6
【解析】因为纸盒中相对两个面上的数互为相反数，
所以观察图形可知，a＝0，b＝2，c＝－6.
(2)【解】(a＋b)c－(b＋c)a＋＝(0＋2)×(－6)－[2＋(－6)]×0＋＝－12－0－＝－12.
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 挑战创新
9．一个正方体的六个面上分别标有数字1，2，3，4，5，6.将它按如图所示的方式顺时针滚动，每滚动90°算一次，则滚动第2 026次后，正方体朝下一面标的数字是________．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX128.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX128.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX128.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX128.tif" \* MERGEFORMAT INCLUDEPICTURE "SX128.tif" \* MERGEFORMAT
【答案】3
【解析】由题图可知：1和6相对，2和5相对，3和4相对，将正方体沿如图所示的方式顺时针滚动，每滚动90°算一次，正方体朝下一面标有的数字依次为2，3，5，4，且依次循环，
因为2 026÷4＝506……2，
所以滚动第2 026次后，正方体朝下一面标有的数字是3.6.1　几何图形
6．1.1　立体图形与平面图形
eq \o(\s\up7(),\s\do5(　　　　　　　))
知识点一　认识立体图形
1．有些几何图形(如长方体、正方体、圆柱、圆锥、球等)的各部分不都在同一平面内，它们是立体图形．
练习1　如图所示，陀螺是由几何体(　)组合而成的．
A．圆和三角形
B．圆柱和圆锥
C．长方体和圆锥
D．长方形和三角形
总结　从各种物体抽象出的几何图形，不考虑它们的颜色、质量和材质，只关注它们的形状、大小和位置关系．
知识点二　认识平面图形
2．有些几何图形(如线段、角、三角形、长方形、圆等)的各部分都在同一平面内，它们是平面图形．
练习2　下面的四个几何图形中，表示平面图形的是(　).
eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( ))
总结　平面图形是由在同一平面内的点和线(直线或曲线)组成的图形．如直线、射线、线段、角、三角形、长方形、平行四边形、梯形、圆等．
知识点三　从不同方向看立体图形
练习3　从左面观察如图所示的几何体，得到的平面图形是(　).
eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( ))
总结　从不同方向看立体图形
知识点四　立体图形的展开图
3．有些立体图形是由一些平面图形围成的，将它们的表面适当展开，可以展开成平面图形．这样的平面图形称为相应立体图形的展开图．
练习4　下面的平面展开图与图下方的立体图形名称不相符的是(　).
eq \o(\s\up7(),\s\do5(A.正方体)) 　　 eq \o(\s\up7(),\s\do5(B.长方体))
eq \o(\s\up7(),\s\do5(C.三棱锥　)) 　　 eq \o(\s\up7(),\s\do5(D.圆柱体))
【解析】选项C中的图形折叠后成为三棱柱，不是三棱锥，因此选项C符合题意．故选C.
总结　由立体图形展开图可以识别立体图形的形状，展开图中有圆形，一般考虑圆柱或圆锥；展开图中有三角形，一般考虑棱柱或棱锥；展开图中只有长方形或正方形，一般考虑长方体或正方体；展开图中有扇形，一般考虑圆锥．
eq \o(\s\up7(),\s\do5(　　　　　　　))
基础巩固
1．下面几何体中，是圆柱的为(　).
eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( ))
2．下列图形是棱锥侧面展开图的是(　).
eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( ))
3．如图所示的六角螺母，从上面看，得到的图形是(　).
eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( ))
4．下图是一正方体的表面展开图．将其折叠成正方体后，与顶点K距离最远的顶点是(　).
A．A点 B．B点
C．C点 D．D点
5．用棱长相同的小正方体摆成如图所示的几何体，第1层有1个正方体，第2层有3个正方体，第3层有6个正方体，按图中摆放的方法类推，第20层有________个正方体．
能力达标
6．如图所示，在一个正方体展开图六个面上依次书写“明”“天”“开”“心”“幸”“福”，则折叠后与“明”相对的是(　).
A．心 B．幸
C．福 D．天
7．下列四个几何体中，从上面看与从左面看的图形相同的几何体有(　).
A．1个 B．2个
C．3个 D．4个
8．下图是一个长方体墨水瓶纸盒的表面展开图，已知纸盒中相对两个面上的数互为相反数．
(1)填空：a＝________，b＝________，c＝________；
(2)求(a＋b)c－(b＋c)a＋的值．
挑战创新
9．一个正方体的六个面上分别标有数字1，2，3，4，5，6.将它按如图所示的方式顺时针滚动，每滚动90°算一次，则滚动第2 026次后，正方体朝下一面标的数字是________．

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