Question

the proof that ( \triangle efg cong \triangle jhg ) is shown.
given: ( g ) is the midpoint of ( overline{hf} ), ( overline{ef} parallel overline{hj} ), and ( overline{ef} cong overline{hj} ).
prove: ( \triangle efg cong \triangle jhg )
what is the missing statement in the proof?
( angle gef cong angle jhg )
( angle feg cong angle hjg )
( angle gfe cong angle ghj )
( angle egf cong angle jgh )

Explanation:

Step1: Use the property of parallel lines

Since \( \overline{EF}\parallel\overline{HJ}\), by the alternate - interior angles theorem, when two parallel lines are cut by a transversal, the alternate interior angles are congruent. Here, the transversal is \( \overline{FH}\), so \( \angle GFE\) and \( \angle GHJ\) are alternate interior angles.

Answer:

\(\angle GFE\cong\angle GHJ\)