配套习题- 矩形性质的应用 -【青果学院】

1/5单选题

难度：

1.

如图，在矩形ABCD中，DE⊥AC于E，∠EDC：∠EDA=1：3，且AC=10，则DE的长度是（）

青果学院

A	3
B	5
C
D

正确答案：RA==

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

2/5单选题

难度：

2.

如图，矩形纸片ABCD中，AB=6cm，BC=8cm，现将其沿AE对折，使得点B落在边AD上的点B₁处，折痕与边BC交于点E，则CE的长为（）

青果学院

A	6cm
B	4cm
C	2cm
D	1cm

正确答案：Qw==

PGRpdj7op6PvvJriiLXmsr9BReWvueaKmOeCuULokL3lnKjovrlBROS4iueahOeCuUI8c3ViPjE8L3N1Yj7lpITvvIw8YnI+4oi04oigQj3iiKBBQjxzdWI+MTwvc3ViPkU9OTDCsO+8jEFCPUFCPHN1Yj4xPC9zdWI+77yMPGJyPuWPiOKIteKIoEJBRD05MMKw77yMPGJyPuKItOWbm+i+ueW9okFCRUI8c3ViPjE8L3N1Yj7mmK/mraPmlrnlvaLvvIw8YnI+4oi0QkU9QUI9NmNt77yMPGJyPuKItENFPUJDLUJFPTgtNj0yY20uPGJyPuaVhemAiUMuPC9kaXY+

3/5单选题

难度：

3.

如图，在矩形ABCD中，对角线AC、BD相交于点O，过O的直线EF分别交AB、CD于点E、F. 若图中阴影部分的面积为6，则矩形ABCD的面积为（）

青果学院

A	12
B	18
C	24
D	30

正确答案：Qw==

PGRpdj7op6PvvJriiLXnn6nlvaJBQkNE77yMPGJyPuKItE9BPU9D77yMQULiiKVEQ++8jDxicj7iiLTiiKBEQ0E94oigQ0FC77yM4oigQ0ZFPeKIoEFFRu+8jDxicj7iiLTilrNDRk/iiYzilrNBRU/vvIw8YnI+4oi04pazQ0ZP55qE6Z2i56ev562J5LqO4pazQUVP55qE6Z2i56ev77yMPGJyPuKIteWbvuS4remYtOW9semDqOWIhueahOmdouenr+S4ujbvvIw8YnI+4oi04pazQU9C55qE6Z2i56ev5pivNu+8jDxicj7iiLXnn6nlvaJBQkNE77yMT0I9T0TvvIw8YnI+4oi055+p5b2iQUJDROeahOmdouenr+aYrzTDlzY9MjQuPGJyPuaVhemAiUMuPC9kaXY+

4/5单选题

难度：

4.

在矩形ABCD中，AB=1，AD=，AF平分∠DAB，过C点作CE⊥BD于E，延长AF、EC交于点H，下列结论中：①AF=FH；②BO=BF；③CA=CH；④BE=3ED，正确的个数是（）

青果学院

A	1
B	2
C	3
D	4

正确答案：Qw==

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

5/5单选题

难度：

5.

如图，矩形ABCD的面积为20cm²，对角线交于点O；以AB、AO为邻边做平行四边形AOC₁B，对角线交于点O₁；以AB、AO₁为邻边做平行四边形AO₁C₂B；…；依此类推，则平行四边形AO₄C₅B的面积为（）

青果学院

A
B
C
D

正确答案：Qg==

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