冀教版九上27.2《圆心角和圆周角》word学案1

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第二十七章圆（一）

27.2圆心角和圆周角（一）

主备人：张永彬 _____年级_____班 学生姓名：______

一、 学习目标：知道圆心角的概念

体会圆心角性质的推导过程

能够运用圆心角的性质进行问题的解答

学习重点：理解掌握并能够运用圆心角的性质进行问题的解答

学习难点：灵活运用圆心角的性质结合圆的基本性质对相关的问题情境进行解答

二、自主预习：

阅读课本的第8页的内容，试完成下列题目

1、我们把____________________________叫做圆心角。如图，在⊙O 中，圆心角是

__________，圆心角所对的弦是__________，圆心角所对的弧是__________

O

CD 分别相等

（2）如果AB=CD （或弧AB 等于弧CD ）那么∠AOB 等于∠COD 吗？为什么？

3、如图，⊙O 1和⊙O

2是两个等圆，如果∠AO 1B=∠CO 2D ，那么AB 与CD ，弧AB 和弧CD 分别相等吗？反过来，如果如果AB=CD （或弧

AB 等于弧CD ）那么∠AO 1B 等于∠CO 2D 吗？为什么？

由此我们可以得到：在同圆或等圆中，相等的圆心角所对的弦______，相等的圆心角所对的弧_______，相等的弦或相等的弧所对的圆心角______，

三、尝试练习

O 中，弦

5、如图，在⊙O 中，已知弧AB=弧CD,请说明AC=BD

6、如图，在⊙O 中，已知AD=BC ，试说明AB=CD 的理由

四、归纳总结

5题图 6题图

通过以上的练习我知道：在同圆或等圆中，相等的圆心角所对的弦______，相等的圆心角所对的弧_______，相等的弦或相等的弧所对的圆心角______

五、当堂检测

7、如图，⊙A 、⊙B 、⊙C 、⊙D 、⊙E 相互外离，它们的半径都为1.

顺次连接五个圆心得到五边形ABCDE ，则图中五个阴影部分的面积

之和是 ；

8、如图，是一块圆形砂轮破碎后的部分残片，试找出它的圆心．

9、某居民小区一处圆柱形的输水管道破裂，维修人员为更换管道，需确定管道圆形截面的半径，下面是水平放置的破裂管道有水部分的截面．

（1）请你补全这个输水管道的圆形截面；

（2）若这个输水管道有水部分的水面宽16cm AB

，求这个圆形截

面的半径．

六、拓展提高(课后作业) 13、课本第9页习题1、2、3题

七、教（学）后记

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