Chapter 12.6, Problem 10E

To determine

To find: Whether we use the given information to prove the triangle $ABC$ and triangle $DEF$ are congruent.

Answer to Problem 10E

The given triangles are not congruent.

Explanation of Solution

Given information:

The given information is

  $\begin{array}{l}<C\cong <F,\\ AB\cong \text{}<DE,\\ BC\cong EF\end{array}$

Here, the two triangles $ABC$ and $DEF$ are given.

In triangle $ABC$ and triangle $DEF$ ,

  $\begin{array}{l}<C\cong <F,\\ AB\cong \text{}<DE,\\ BC\cong EF\end{array}$

Hence,

It follows the criteria of $SSA$ , being two pairs of congruent sides and one pair of non-included angle the given information does not prove the congruency of given triangles.

Therefore, the given triangle are not congruent as it follows the $SSA$ criteria.