Chapter 12, Problem 16CR

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 16CR

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

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Recollect the HL Congruence Theorem:

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of second right triangle, then the two triangles are congruent.

From the given figure, the triangles $\Delta WXZ$ and $\Delta YZX$ are two right triangles with $\overline{WX}\cong \overline{YZ}$ .

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

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