Chapter 4, Problem 10PT

To determine

To Prove:

  $△\mathrm{X}\mathrm{W}\mathrm{Z}\cong △\mathrm{Z}\mathrm{Y}\mathrm{X}$

Explanation of Solution

Give information:

  

Proof:

Given segment $\mathrm{X}\mathrm{Y}$ is parallel to segment $\mathrm{W}\mathrm{Z}$ yields angle $2$ is congruent to angle $4$ .

Given segment $\mathrm{X}\mathrm{W}$ is parallel to segment $\mathrm{Y}\mathrm{Z}$ yields angle $1$ is congruent to angle $3$ .

By the reflective property segment $\mathrm{X}\mathrm{Z}$ is congruent to itself.

Triangle $\mathrm{X}\mathrm{W}\mathrm{Z}$ is congruent to triangle $\mathrm{Z}\mathrm{Y}\mathrm{X}$ by the angle side angle postulate.