Chapter 15, Problem 22RP

To determine

To conclude: that $XV>VY$ as shown in the given figure.

Answer to Problem 22RP

  $XV>VY$ .

Explanation of Solution

Given:

A triangle in which $\overline{ZX}\cong \overline{ZY},WX<WY$ .

  

Calculation:

According to the question, a triangle in which $\overline{ZX}\cong \overline{ZY},WX<WY$ . Now,

  $\begin{array}{l}\overline{ZX}\cong \overline{ZY}\left\{\text{given}\right\}\\ WX<WY\left\{\text{given}\right\}\\ \overline{WZ}\cong \overline{WZ}\left\{\text{reflexive group}\right\}\\ \angle WZX<\angle WZY\left\{\text{converse of hinge theorem}\right\}\\ \Rightarrow \angle WZY>\angle WZX\\ \angle XZV>\angle YZV\{\text{Special subtraction property}}\\ \overline{ZV}\cong \overline{ZV}\left\{\text{reflexive group}\right\}\\ \therefore XV>VY\left\{\text{by hinge theorem}\right\}\end{array}$

Thus, $XV>VY$