Chapter 8.4, Problem 2PSA

To determine

To prove : The equality of $\frac{AZ}{AX}$ with respect to $\frac{ZY}{ZX}$ .

Explanation of Solution

Given information : Here, we have given that $\angle X\cong \angle ZBA$

Proof: In $\Delta ZYX$ and $\Delta ZBA$

  $\angle X\cong \angle ZBA$ (Given)

  $\angle Z\cong \angle Z$ (Common)

  $\Rightarrow \Delta ZYX\sim \Delta ZBA$ (By AA Similarity Rule)

  $\Rightarrow \frac{AZ}{ZY}=\frac{AB}{XY}$ (Corresponding sides of similar triangles are equal in ratio)

Or, $\frac{AZ}{AB}=\frac{ZY}{XY}$