Chapter 12, Problem 21CR

To determine

To explain: The way to prove $\angle K\cong \angle N$ .

Answer to Problem 21CR

The method to prove $\angle K\cong \angle N$ is explained below.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

From the given figure, it can be observed that $\overline{HJ}\cong \overline{LM}$ , $\angle J\cong \angle M$ , and $\overline{JK}\cong \overline{LM}$ .

By Alternate Interior Angles Theorem, $\angle XZW\cong \angle XZY$ .

So, by SAS Congruence Theorem, $\Delta HJK\cong \Delta LMN$ .

Therefore, the corresponding parts of congruent triangles are congruent, so $\angle K\cong \angle N$ .