Chapter 1.6, Problem 55SPR

To determine

To check the assumption made

Answer to Problem 55SPR

Yes, $\angle PLN\cong \angle NLM$

Explanation of Solution

Given information:

A figure and assumption: $\angle PLN\cong \angle NLM$

  

According to figure,

The line $LP,MN$ are equal because the $\angle LPN$ is at $90°$ and both lines are straight. Similarly,

The line $PN$ and $MN$ are also same.

Now, taking triangles $LPN$ and $LMN$ ,

  $\angle LPN=\angle LMN$......(1)

And, $LP=MN$..... (2)

And, $PN=MN$...... (3)

Hence, both triangle are congruent. So,

  $\angle PLN\cong \angle NLM$

Due to corresponding part of congruent Triangles.

Yes, assumption is correct.