Chapter 4.5, Problem 11CE

To determine

Name a pair of overlapping triangles.Tell whether the triangles are congruent by the SSS, SAS , ASA, AAS , or HL method.

Answer to Problem 11CE

By ASA Postulate , $\Delta LMN\cong \Delta \text{PNM}$

Explanation of Solution

Given:

  $\angle 2\cong \angle 3$

  $\angle 1\cong \angle 4$

Calculation:

The diagram is :

  

Consider the $\Delta LMN\text{ and }\Delta \text{PNM}$ :

  $\begin{array}{l}\angle 2\cong \angle 3\\ \Rightarrow \angle NMP\cong \angle MNL\end{array}$

  $\overline{MN}\cong \overline{NM}$

  $\angle 2\cong \angle 3$

  $\angle 1\cong \angle 4$

So,

  $\begin{array}{l}\angle 2+\angle 1\cong \angle 3+\angle 4\\ \Rightarrow \angle LMN\cong \angle PNM\end{array}$

So, by ASA Postulate , $\Delta LMN\cong \Delta \text{PNM}$

Hence proved.