Chapter 15.3, Problem 2PSA

To determine

To Find: The larger angle of the given triangle.

Answer to Problem 2PSA

  $\angle R$

Explanation of Solution

Given:

  $\begin{array}{l}\to \overline{QR}\cong \overline{XY}\\ \to \overline{PR}\cong \overline{WY}\\ \to \overline{PR}=15\\ \to \overline{WX}=12\\ \therefore \overline{PR}>\overline{WX}\end{array}$

  

Concept:

The Converse Hinge Theorem: It states that if two sides of one triangle is congruent to another triangle and third side is greater than another then the angle opposite to greater one will be greater than the another.

Calculation:

  $\begin{array}{l}\to \overline{QR}\cong \overline{XY}\text{}\left(\text{Given}\right)\\ \to \overline{PR}\cong \overline{WY}\left(\text{Given}\right)\\ \to \overline{PR}=15\left(\text{Given}\right)\\ \to \overline{WX}=12\left(\text{Given}\right)\\ \therefore \overline{PR}>\overline{WX}\\ \text{⇒}\text{Conclusion : }\angle R>\angle Y\left(\text{The converse Hinge theorem or SSS inequaliy theorem}\right)\end{array}$

Conclusion:

Thus the $\angle R>\angle Y$