Question

the proof that δefg ≅ δjhg is shown. what is the missing statement in the proof? given: g is the midpoint of hf, ef ∥ hj, and ef ≅ hj. prove: δefg ≅ δjhg. options: ∠feg ≅ ∠hjg, ∠gfe ≅ ∠ghj, ∠egf ≅ ∠jgh, ∠gef ≅ ∠jhg

Explanation:

G is the midpoint of $\overline{HF}$, so $\overline{FG} \cong \overline{HG}$. Given $\overline{EF} \cong \overline{HJ}$ and $EF \parallel HJ$, the alternate interior angles formed by transversal $\overline{HF}$ cutting parallel lines $EF$ and $HJ$ are congruent. These angles are $\angle FEG$ (at E on $\overline{EF}$) and $\angle HJG$ (at J on $\overline{HJ}$). This gives two sides and the included angle for SAS congruence.

Answer:

A. $\angle FEG \cong \angle HJG$