Question

use the given information to prove that ef = fj. given: eg = hj, fg = hf. prove: ef = fj

Explanation:

Step1: Express line - segment relationships

We know that $EG=EF + FG$ and $HJ = HF+FJ$ since a line - segment is the sum of its sub - segments.

Step2: Substitute given equalities

Given $EG = HJ$ and $FG=HF$, substituting into the above equations gives $EF + FG=HF + FJ$.

Step3: Use subtraction property

Subtract $FG$ (which is equal to $HF$) from both sides of the equation $EF + FG=HF + FJ$. We get $EF=FJ$.

Answer:

$EF = FJ$ (proven)