Chapter 12, Problem 18CR

To determine

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

Answer to Problem 18CR

The $\Delta TUV$ and $\Delta QRS$ are not congruent.

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

By AAS Congruence Theorem:

If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

From the given figure, it can be observed that $\angle T\cong \angle Q$ , and $\overline{TU}\cong \overline{QR}$ .

So, there is only enough information to conclude that one pair of angles and one pair of sides are congruent.

Therefore, the $\Delta TUV$ and $\Delta QRS$ are not congruent.