Question

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


BE
AD
JB
BC

Answer 1

JA / JC = AB / BC because, as we can see in the picture above, it's the same proportion. So the answer is the fourth one - BC.

I hope that's what you meant and if so that it will help you :)

Answer 2

Given: AC, DF, and GI are parallel.

Solution:

In ΔJAB and ΔJDE

∠J is common.

∠JAB=∠JDE→→As, AB║DE, so corresponding angles are equal.

ΔJAB ~ ΔJDE→→[AA similarity]

Similarly, we can prove that, ΔJ C B and ΔJ FE by AA similarity.

As, we know when triangles are similar their sides are proportional.

`(JA)/(JD)=(JB)/(JE)=(AB)/(DE)\\\\ (JB)/(JE)=(JC)/(JF)=(BC)/(EF)`

`(JA)/(AB)=(1)/(JE)\\\\(JC)/(BC)=(1)/(JE)\\\\(JA)/(AB)=(JC)/(BC)\\\\= (JA)/(JC)=(AB)/(BC)`

Option 4: BC is correct choice.