Answer:
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
[tex]\frac{JD}{AD}=\frac{JE}{BE}[/tex]
Because AC is parallel to DF and A and B are the mid points of JD and JE
[tex]\frac{JD}{GD}=\frac{JE}{EH}[/tex]
Because DF is parallel to GI
Divide equation one by equation second then we get
[tex]\frac{GD}{AD}=\frac{EH}{BE}[/tex]
Adding one on both sides then we get
[tex]\frac{GD}{AD}+1=\frac{BE}{EH}+1[/tex]
[tex]\frac{GD+AD}{AD}=\frac{BE+EH}{BE}[/tex]
[tex]\frac{AG}{AD}=\frac{BH}{BE}[/tex]
Because BE+EH=BH and AD+GD=AG
Reciprocal on both sides then we get
[tex]\frac{AD}{AG}=\frac{BE}{BH}[/tex]
Hence, option C is true.
