Chapter 12, Problem 19CR

To determine

To decide: Whether the given information is enough to prove that $\Delta LPN\cong \Delta LMN$ using the ASA Congruence Theorem. If so write a proof if not then explain the reason.

Answer to Problem 19CR

The $\Delta LPN$ and $\Delta LMN$ are congruent.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

By ASA Congruence Theorem:

If two angles and a included side of one triangle are congruent to the two angles and the corresponding included side of a second triangle, then the two triangles are congruent.

From the given figure, it can be observed that $\angle PLN\cong \angle MLN$ , and $\angle LNP\cong \angle LNM$ .

By Reflexive Property of Congruence, $\overline{LN}\cong \overline{LN}$ .

Therefore, the $\Delta LPN$ and $\Delta LMN$ are congruent.