多边形及其内角和(含答案).pdf

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1、1/5 73 多边形及其内角和基础过关作业1四边形ABCD中，如果 A+C+D=280，则 B的度数是（）A80 B90 C170 D202一个多边形的内角和等于1080，这个多边形的边数是（）A9 B8 C7 D6 3内角和等于外角和2 倍的多边形是（）A五边形 B六边形 C七边形 D八边形4六边形的内角和等于_度5正十边形的每一个内角的度数等于_，每一个外角的度数等于_6如图，你能数出多少个不同的四边形？7四边形的四个内角可以都是锐角吗？可以都是钝角吗？可以都是直角吗？?为什么？8求下列图形中x 的值：2/5 综合创新作业9（综合题）已知：如图，在四边形ABCD中，A=C=90，BE平分

2、ABC，?DF平分ADC BE与 DF有怎样的位置关系？为什么？10（应用题）有10 个城市进行篮球比赛，每个城市均派3 个代表队参加比赛，规定同一城市间代表队不进行比赛，其他代表队都要比赛一场，问按此规定，?所有代表队要打多少场比赛？11（创新题）如图，以五边形的每个顶点为圆心，以1 为半径画圆，求圆与五边形重合的面积12（1）（2005 年，南通）已知一个多边形的内角和为540，则这个多边形为（）A三角形 B四边形 C五边形 D六边形（2）（2005 年，福建泉州）五边形的内角和等于_度13（易错题）一个多边形的每一个顶点处取一个外角，这些外角中最多有钝角（?）A1个 B2 个 C3 个

3、D4 个文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8

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7、G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8

8、 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4

9、G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F83/5 培优作业14（探究题）（1）四边形有几条对角线？五边形有几条对角线？六边形有几条对角线？猜想并探索：n 边形有几条对角线？（2）一个 n 边形的边数增加1，对角线增加多少条？15（开放题）如果一个多边形的边数增加1，?那么这个多边形的内角和增加多少度？若将 n 边形的边数增加1 倍，则它的内角和增加多少度？数学世界攻其不备壁虎在一座油罐的下底

10、边沿A 处它发现在自己的正上方油罐上边缘的B?处有一只害虫壁虎决定捕捉这只害虫为了不引起害虫的注意，它故意不走直线，而是绕着油罐，沿着一条螺旋路线，从背后对害虫进行突然袭击如图7-3-5 结果，?壁虎的偷袭得到成功，获得了一顿美餐请问：壁虎沿着螺旋线爬行是最短的路程吗（线段AB除外）？文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G

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12、HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G

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15、3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8

16、HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F84/5 答案:1A 点拨：B=360-（A+C+D）=360-280=80

17、故选A2B 点拨：设这个多边形的边数为n，则（n-2）180=1080解得 n=8故选 B3 B 点拨：设这个多边形的边数为n，根据题意，得（n-2）180=2 360解得n=6故选 B4720 5144；36点拨：正十边形每一个内角的度数为：(102)18010=144，每一个外角的度数为：180-144=366有 27 个不同的四边形7解：四边形的四个内角不可以都是锐角，不可以都是钝角，可以都是直角因为四边形的内角和为360，如果四个内角都是锐角或都是钝角，?则内角和小于360或大于360，与四边形的内角和为360矛盾?所以四个内角不可以都是锐角或都是钝角若四个内角都是直角，则四个内角的和

18、等于360，与内角和定理相符，所以四个内角可以都是直角8解：（1）90+70+150+x=360解得 x=50（2）90+73+82+（180-x）=360解得 x=65（3）x+（x+30）+60+x+（x-10）=（5-2）180解得 x=1159解：BE DF理由：A=C=90，A+C=180 ABC+ADC=360 -180=180 ABE=12ABC，ADF=12ADC，ABE+ADF=12（ABC+ADC）=12 180=90又 ABE+AEB=90，AEB=ADF，BE DF（同位角相等，两直线平行）10解：12n（n-3）=1210（10-3）=12107=35（场）答：按此规

19、定，所有代表队要打35 场比赛点拨：问题类似于求多边形对角线的个数文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E

20、6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC

21、9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E

22、6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC

23、9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E

24、6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC

25、9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F85/5 11解：（5-2）180 360 12=1.5 点拨：不能直接求出扇形的度数，用整体法圆与五边形重合部分的角度和正好是五边形的内角和12（1）C 点拨：设这个多边形的边数为n，依题意，得（n-2）180=540，解得n=5，故选 C（2）540 点拨：（n-2）180=（5-3）180

26、=54013C 14解：（1）四边形有2 条对角线；五边形有5 条对角线；六边形有9 条对角线；n边形有(3)2n n条对角线（2）当 n 边形的边数增加1 时，对角线增加（n-1）条点拨：从n 边形的一个顶点出发，向其他顶点共可引（n-3）条对角线，n 个顶点共可引n（n-3）条，但这些对角线每一条都重复了一次，故n 边形的对角线条数为(3)2n n15180，n180数学世界答案:是最短的路程可用纸板做一个模型，沿AB剪开便可看出结论文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F

27、8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI

28、2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F

29、8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI

30、2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F

31、8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI

32、2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8文档编码:CC9H8Z7Q6R8 HI2O8D4R4E6 ZO1A1A4G3F8