Chapter 12.6, Problem 7E

To determine

To find: The third statement needed to prove the triangles $FGH$ and $LMN$ are congruent.

Answer to Problem 7E

The given triangle are congruent by $AAS$ criteria.

Explanation of Solution

Given information:

The given information is side $GH\cong MN$ and $<G\cong <M$

Here, the two triangles $FGH$ and $LMN$ are given.

By using $AAS$ criteria, one more angle is needed to prove the congruency of triangle $FGH$ and triangle $LMN$ . Thus,

  $\begin{array}{l}<F\cong <L,\\ <G\cong <M,\\ GH\cong MN\end{array}$

Hence,

The given triangle $FGH$ and $LMN$ are congruent by $AAS$ criteria.

Therefore, the given triangle are congruent by $AAS$ criteria.