1 . 下图是小明复习全等三角形时遇到的一个问题并引发的思考,请帮助小明完成以下学习任务.
如图,OC平分
,点P在OC上,M、N分别是
、OB上的点,
,求证:
.
小明的思考:要证明
,只需证明
即可.
证法:如图①:∵OC平分
,∴
,
又∵
,
,∴
,
∴
;
请仔细阅读并完成以下任务:
![](https://img.xkw.com/dksih/QBM/2022/5/3/2971556652843008/2974950110486528/STEM/93b06bfd-3171-47a5-9d77-19e02cb916d0.png?resizew=524)
(1)小明得出
的依据是______(填序号).
①SSS ②SAS ③AAS ④ASA ⑤HL
(2)如图②,在四边形ABCD中,
,
的平分线和
的平分线交于CD边上点P,求证:
.
(3)在(2)的条件下,如图③,若
,
,当△PBC有一个内角是45°时,
的面积是______.
如图,OC平分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2032fccdf9ab12429aae024d67b19d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acd79bb9fb06f7c806eb6e17e4b613.png)
小明的思考:要证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acd79bb9fb06f7c806eb6e17e4b613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d54326f92838c51a197cc82985e506.png)
证法:如图①:∵OC平分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1f18cef1745d84a0265246684753bd.png)
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ce5cddb3791c46d6ef0c32d35a7886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2032fccdf9ab12429aae024d67b19d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905a8192e8d6365309562606283e9959.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acd79bb9fb06f7c806eb6e17e4b613.png)
请仔细阅读并完成以下任务:
![](https://img.xkw.com/dksih/QBM/2022/5/3/2971556652843008/2974950110486528/STEM/93b06bfd-3171-47a5-9d77-19e02cb916d0.png?resizew=524)
(1)小明得出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905a8192e8d6365309562606283e9959.png)
①SSS ②SAS ③AAS ④ASA ⑤HL
(2)如图②,在四边形ABCD中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609ada36dd56b33279103ebc1f90bbac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4189a0821a0ffab9dc171ecd279ba442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
(3)在(2)的条件下,如图③,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcd54ff42ebdc70cb273cd5909d549f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
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