Question

AC, DF, and GI are parallel. Use the figure to complete the proportion. (7)

Answer 1

Option C

Explanation:

We have to find the value in the blank space

We are given that AC,DF and GI are parallel

We know that by middle splitting theorem

We have

`(JD)/(AD)=(JE)/(BE)`

Because AC is parallel to DF and A and B are the mid points of JD and JE

`(JD)/(GD)=(JE)/(EH)`

Because DF is parallel to GI

Divide equation one by equation second then we get

`(GD)/(AD)=(EH)/(BE)`

Adding one on both sides then we get

`(GD)/(AD)+1=(BE)/(EH)+1`

`(GD+AD)/(AD)=(BE+EH)/(BE)`

`(AG)/(AD)=(BH)/(BE)`

Because BE+EH=BH and AD+GD=AG

Reciprocal on both sides then we get

`(AD)/(AG)=(BE)/(BH)`

Hence, option C is true.

Answer 2

The answer is

C.) BE

AD/AG=BE/BH