配套习题- 勾股定理“助力”几何证明（一） -【青果学院】

1/5单选题

难度：

1.

在中，分别为的中点，，求的长为（）

A
B
C
D

正确答案：QQ==

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

2/5单选题

难度：

2.

已知，如图，△ABC和△ECD都是等腰直角三角形，∠ACB=∠DCE=90°，D为AB边上一点. 则BD与AE的关系是（）

A	BD=AE
B	BD=2AE
C
D

正确答案：QQ==

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

3/5单选题

难度：

3.

已知：如图，在四边形ABCD中，∠ABC=90°，CD⊥AD，则AB与BC的关系为（）

A	AB=BC
B	AB=2BC
C
D

正确答案：QQ==

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

4/5单选题

难度：

4.

如图，△ACB和△ECD都是等腰直角三角形，∠ACB=∠ECD=90°，D为AB边上一点，则AD，DB，DE的数量关系为（）

A
B
C
D

正确答案：Qw==

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

5/5单选题

难度：

5.

如图. 矩形纸片ABCD中，已知AD=8，折叠纸片使AB边与对角线AC重合，点B落在点F处，折痕为AE，且EF=3. 则AB的长为（　　）

A	3
B	4
C	5
D	6

正确答案：RA==

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