Question

$overline{gh} cong overline{ef}$ and $overline{ef} parallel overline{gh}$. complete the proof that $\triangle efg cong \triangle ghe$.

	statement	reason
2	$overline{ef} parallel overline{gh}$	given
3	$angle egh cong angle feg$	alternate interior angles theorem
4

Explanation:

Step1: Identify shared side

$\overline{EG} \cong \overline{GE}$ (Reflexive Property of Congruence)

Step2: Apply SAS congruence

We have $\overline{GH} \cong \overline{EF}$, $\angle EGH \cong \angle FEG$, and $\overline{EG} \cong \overline{GE}$. By the Side-Angle-Side (SAS) Congruence Postulate, $\triangle EFG \cong \triangle GHE$.

Completed Proof Table Row 4:

Statement	Reason
$\triangle EFG \cong \triangle GHE$	Side-Angle-Side (SAS) Congruence Postulate

Answer:

$\triangle EFG \cong \triangle GHE$