Chapter 15.3, Problem 5PSA

To determine

To Prove: The side XY is greater than ZY in the given figure.

Explanation of Solution

Given:

  $\begin{array}{l}\to \overline{WX}\cong \overline{WZ}\\ \to \angle XWY>\angle ZWY\end{array}$

  

Concept:

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

Calculation:

  $\begin{array}{l}\to \overline{WX}\cong \overline{WZ}\left(\text{Given}\right)\\ \to \angle XWY>\angle ZWY\left(\text{Given}\right)\\ \text{⇒}XY>ZY\left(\text{ SAS inequality theorem}\right)\end{array}$

Conclusion:

Thus,from the given condition and using SAS inequality theorem it is proved that $XY>ZY$