Question

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

Answer 1

Answer:

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.

$\frac{JA}{JD}=\frac{JB}{JE}=\frac{AB}{DE}\\\\ \frac{JB}{JE}=\frac{JC}{JF}=\frac{BC}{EF}$

$\frac{JA}{AB}=\frac{1}{JE}\\\\\frac{JC}{BC}=\frac{1}{JE}\\\\\frac{JA}{AB}=\frac{JC}{BC}\\\\= \frac{JA}{JC}=\frac{AB}{BC}$

Option 4: BC is correct choice.

Answer 2

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 :)