配套习题- 如何解决矩形中的折叠问题 -【青果学院】

1/5单选题

难度：

1.

如图，矩形ABCD的边长AB=6，BC=8，将矩形折叠，使点C与点A重合，则折痕EF长为（）。

A	3
B
C	4
D

正确答案：Qg==

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

2/5单选题

难度：

2.

如图，矩形纸片ABCD中，AB=4，AD=3，折叠纸片使AD边与对角线BD重合，折痕为DG，则AG的长为（）。

A
B	1
C
D

正确答案：QQ==

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

3/5单选题

难度：

3.

将矩形纸片ABCD按如图所示的方式折叠，得到菱形AECF. 若AB=6，则BC的长为（）

A	1
B
C
D	12

正确答案：Qw==

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

4/5单选题

难度：

4.

折叠矩形纸片ABCD，先折出折痕（对角线）BD，再折叠AD边与对角线BD重叠，得折痕DG，若AB=2BC=1，则AG的长为（　　）

A
B
C
D

正确答案：RA==

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

5/5单选题

难度：

5.如图所示，在矩形纸片ABCD中，已知AB：BC=2：3，点M在BC边上，将矩形折叠，使点D落在点M处，折痕为EF，若AE=2，CM=4，则AB的长为（）

A	6
B	8
C	10
D	12

正确答案：Qg==

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