Mathematics: Ac, df, and gi are parallel. use the figure to complete the proportion. (7)

Ac, df, and gi are parallel. use the figure to

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13.03.2022

Option C

Step-by-step 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

$\frac{JD}{AD}=\frac{JE}{BE}$

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

$\frac{JD}{GD}=\frac{JE}{EH}$

Because DF is parallel to GI

Divide equation one by equation second then we get

$\frac{GD}{AD}=\frac{EH}{BE}$

Adding one on both sides then we get

$\frac{GD}{AD}+1=\frac{BE}{EH}+1$

$\frac{GD+AD}{AD}=\frac{BE+EH}{BE}$

$\frac{AG}{AD}=\frac{BH}{BE}$

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

Reciprocal on both sides then we get

$\frac{AD}{AG}=\frac{BE}{BH}$

Hence, option C is true.

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