Chapter 4.5, Problem 13WE

To determine

To state: The pair of congruent parts and method that is used to prove the congruency of triangles $△QPY\text{ and }△TPX$

Answer to Problem 13WE

The triangles $△QPY\text{ and }△TPX$ are congruent by "Angle Side Angle "property.

Explanation of Solution

Given information:

System information: $\begin{array}{l}\angle 3\cong \angle 4\\ \angle 5\cong \angle 6\end{array}$

System figure:

  

Calculation:

Considering the information provided are as follow:

  $\begin{array}{l}\angle 3\cong \angle 4\\ \angle 5\cong \angle 6\end{array}$

Consider the following two tringles:

  $△QPY\text{ and }△TPX$

From the figure and provided data,

  $\begin{array}{l}\overline{PQ}\cong \overline{PT}\\ \angle 5\cong \angle 6\\ \angle 3\cong \angle 4\end{array}$

Hence, the triangles $△QPY\text{ and }△TPX$ are congruent by Angle Side Angle property.