Chapter 9.5, Problem 12WE

To determine

To prove: $\Delta UXZ\sim \Delta YVZ$

Explanation of Solution

Given information:

Calculation:

Note that in a circle, two inscribed angles with the same intercept arc are congruent.

This implies that,

  $\begin{array}{l}\angle XUZ\approx \angle VYZ\\ \angle UXZ\cong \angle YVZ\end{array}$

Also, it can be concluded that,

  $\angle UZX\cong \angle YZV$

Therefore, by the use of AA similarity criterion, it follows that $\Delta UXZ\sim \Delta YVZ$ .