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 :)
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.
J D J A = J E J B = D E A B J E J B = J F J C = EF BC
A B J A = J E 1 BC J C = J E 1 A B J A = BC J C = J C J A = BC A B
Option 4: BC is correct choice. ;
The question invites us to complete a proportion formed by parallel lines and similar triangles. Using the properties of similar triangles, we determine that the segment BC completes the proportion with the other given segments. Therefore, BC is the answer to the question.
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