Chapter 12, Problem 9CR

To determine

To decide: Whether the given information is enough to prove that $\Delta WXZ\simeq \Delta YZX$ using the SAS Congruence Theorem. If so write a proof if not then explain the reason.

Answer to Problem 9CR

The $\Delta WXZ$ , and $\Delta YZX$ are congruent.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Recollect the SAS Congruence Theorem:

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

From the given figure, it can be observed that $\overline{WX}\simeq \overline{YZ}$ , and $\overline{WZ}\simeq \overline{YX}$ .

By Alternate Interior Angles theorem, $\angle WXZ\cong \angle YZX$ .

By Reflexive Property of Congruence, $\overline{XZ}\cong \overline{XZ}$ .

By SAS Congruence Theorem, $\Delta WXZ\simeq \Delta YZX$ .

Therefore, the $\Delta WXZ$ , and $\Delta YZX$ are congruent.