Chapter 4.5, Problem 11WE

To determine

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

Answer to Problem 11WE

The triangles $△QPR\text{ and }△TPS$ are congruent by SSS property.

Explanation of Solution

Given information:

System information: $\begin{array}{l}\angle 1\cong \angle 2\\ \angle 3\cong \angle 4\\ \overline{QR}\cong \overline{TS}\end{array}$

System figure:

  

Calculation:

Considering the information provided are as follow:

  $\begin{array}{l}\angle 1\cong \angle 2\\ \angle 3\cong \angle 4\\ \overline{QR}\cong \overline{TS}\end{array}$

Consider the following two tringles:

  $△QPR\text{ and }△TPS$

From the figure and provided data,

  $\begin{array}{l}\overline{PQ}\cong \overline{PT}\\ \overline{PR}\cong \overline{PS}\\ \overline{QR}\cong \overline{ST}\end{array}$

Hence, the triangles $△QPR\text{ and }△TPS$ are congruent by SSS property.