Chapter 3.7, Problem 3PSA

To determine

To Prove: The congruency of the $\overline{RW}$ with respect to $\overline{RZ}$

Explanation of Solution

Given information: $\overline{SX}\cong \overline{TY}$ , $\overline{WX}\cong \overline{YZ}$ and $\overline{SW}\cong \overline{TZ}$ is provided in the question which will help to find the solution.

Proof: Here, $\overline{SX}\cong \overline{TY}$ ,(given)

  $\overline{WX}\cong \overline{YZ}$ (given)

And, $\overline{SW}\cong \overline{TZ}$ (given)

So that, $\overline{RW}=\overline{RS}+\overline{SW}$

So that, $\Delta SWX\cong \Delta TZY$

So, $\angle 1=\angle 2$

Hence, $\overline{RW}\cong \overline{RZ}$ (opposite angles of equal sides are congruent)