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【329950】12.3.1角平分线的性质(1)

时间:2025-02-07 09:26:20 作者: 字数:2708字

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

12.3.1 角平分线的性质(1

习目标

1、应用全等三角形的知识理解角平分线的原理

2、会利用尺规作一个角的角平分线

3、在利用尺规作图的过程中培养学生的动手操作能力

学习重点:利用尺规作一个角的角平分线

学习难点角平分线作图方法的提炼

课前预习

阅读课本,完成下列的问题:

1、角平分线的尺规作图:做∠AOB的角平分线,并将法补充完整。

1)以_为圆心,___为半径,交OA 于___

OB于 ___

2)分别以___为圆心,大于___为半径

画弧,两弧在AOB内部交于点___

3)画___

2、从作图我们可猜想:

角平分线的性质:角的平分线上的__到角的两边的___相等。

课内探究

1、在△ABCC=90°AD平分∠CABBC=8BD=5,那么D到直线AB的距离是___。

2如图, 若点PAOB的角平分线上,若应用角平分线的性质可得到:PA=PB则需要 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 添加的条件是___。

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>


  1. 如图, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 平分 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 上一点,连接 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> .求证:⑴ <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> = <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> .

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>


拓展延伸

1如图所示, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 的平分线, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,且 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,那么 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 相等吗?为什么?

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>



当堂检测

1、如图所示OC是∠AOB 的平分线,P OC上任意一点,PE=PD?为什么?

组合 5



2、如图:在△ABC中,∠C=90°AD是∠BAC的平分线,DEABEFAC上,BD=DF; 求证:CF=EB

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

3、在RtABC中,BD平分∠ABCDEABE,则

图中相等的线段有哪些?相等的角呢?

哪条线段与DE相等?为什么?

AB10BC8AC6,求BEAE的长和△AED的周长。


画布 21






课后训练

1、如图, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 平分 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

则下列结论中正确的有( )① <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ;② <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ;③ <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

A0B1C2D3

2、如图,在 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 中, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 平分 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,连接 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,则下列结论错误的是( )


 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>




A <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> B <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> C <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> D <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

3、如上题图,在 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 中, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 平分 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,且 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,则 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 的周长为( )

A4 B6 C8 D10

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 4、如图,在 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 中, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 平分 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,已知 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,则点 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 的距离为_______cm


 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

5、如图, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 平分 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 延长线于 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,且 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> .求证: <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>



6、如图, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 平分 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,连接 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> .求证: <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>


 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>



7、已知,如图 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 的平分线, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> ,点 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> 上, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a> .求证: <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/904/" title="平分" class="c1" target="_blank">平分</a>