配套习题- 添加平行线证明线段等积式（比例式） -【青果学院】

1/5单选题

难度：

1.

如图，在△ABC中，AB=14，BC=12，AD：DB=4：3，DE∥BC，角平分线BG交DE于点F，则GF：GB的值为（　　）

A	4：3
B	4：7
C	1：13
D	1：14

正确答案：RA==

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

2/5单选题

难度：

2.

如图，D、E是△ABC中BC边的两个三等分点，F是AC的中点，AD与EF交于O，则等于（　　）

A
B
C
D

正确答案：QQ==

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

3/5单选题

难度：

3.

如图，△ABC中，D、E是BC边上的点，BD：DE：EC=3：2：1，M在AC边上，CM：MA=1：2，BM交AD，AE于H，G，则BH：HG：GM等于（　　）

A	3：2：1
B	5：3：1
C	25：12：5
D	51：24：10

正确答案：RA==

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

4/5单选题

难度：

4.

如图，△ABC中，D为BC中点，E为AD的中点，BE的延长线交AC于F，则AF:FC的值为（）

A	1:5
B	1:4
C	1:3
D	1:2

正确答案：RA==

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

5/5单选题

难度：

5.

如图，已知平行四边形ABCD中，E、F分别为边AB、AD上的点. EF与对角线AC交于P， = ，（a、b、m、n均为正数），则的值为（）

A
B
C
D

正确答案：Qw==

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