Chapter 12.3, Problem 14E

To determine

To explain:

The triangles are congruent using the congruence theoem.

Explanation of Solution

Given:

The two triangle

  $\Delta KLM\cong \Delta MNK$

Concept used:

Two geometric figures are congruent if a rigid motion or a composition of rigid motions maps one of the figures onto other.

Calculation:

If two triangles are congruent.

So all the corresponding parts are congruent.

If all corresponding parts of two triangles are congruent.

So the triangle are congruent.

Two pairs of corresponding sides of the included angles of those sides are marked congruent.

By the reflexive property of congruence

  $\begin{array}{l}\overline{KL}\cong \overline{NM}\\ \overline{KM}\cong \overline{MK}\end{array}$

  $\angle N\cong \angle L$

In triangle

  $\begin{array}{l}\Delta KLM\cong \Delta MNK\\ \angle NKM\cong \angle LKM\end{array}$

If two parallel lines are cut by a transversal.

The pair of alternate interior angles are congruent.

  $\angle LKMand\angle NMK$ is not the included

So, the congruence theorem cannot be used.