Question

in exercises 7 and 8, state the third congruence statement that is needed to prove that $\triangle fgh cong \triangle lmn$ using the given theorem.

1. given $overline{gh} cong overline{mn}$, $angle g cong angle m$, _ $cong$ _

use the aas congruence theorem (thm. 5.11).

in exercises 7 and 8, state the third congruence statement that is needed to prove that $\triangle fgh cong \triangle lmn$ using the given theorem.

1. given $overline{fg} cong overline{lm}$, $angle g cong angle m$, _ $cong$ _

use the asa congruence theorem (thm. 5.10).

Explanation:

Step1: Recall AAS Theorem

AAS (Angle-Angle-Side) requires two pairs of congruent angles and one pair of non-included congruent sides.
Given $\overline{GH} \cong \overline{MN}$, $\angle G \cong \angle M$. We need a second pair of congruent angles: $\angle H \cong \angle N$.

Step2: Recall ASA Theorem

ASA (Angle-Side-Angle) requires two pairs of congruent angles and the included congruent side.
Given $\overline{FG} \cong \overline{LM}$, $\angle G \cong \angle M$. We need the other included side pair: $\overline{GH} \cong \overline{MN}$.

Answer:

1. $\boldsymbol{\angle H \cong \angle N}$
2. $\boldsymbol{\overline{GH} \cong \overline{MN}}$