Chapter 12.3, Problem 12E

To determine

To explain:

The triangles are congruent using the congruence theoem.

Explanation of Solution

Given:

The two triangle

  $\Delta QRV\cong \Delta TSU$

Concept used:

Two geometric figures are congruent if a rigid motion or a composition of rigid motions maps one of the figures onto other.

Calculation:

If two triangles are congruent.

So all the corresponding parts are congruent.

If all corresponding parts of two triangles are congruent.

So the triangle are congruent.

Two pairs of corresponding sides of the included angles of those sides are marked congruent.

By the reflexive property of congruence

  $\begin{array}{l}\overline{QR}\cong \overline{ST}\\ \overline{QV}\cong \overline{UT}\end{array}$

  $\angle V\cong \angle U$

In triangle

  $\Delta QRV\cong \Delta TSU$

Therefore,

The angle marked congruent are not the included angles of the sides marked congruent

So, the congruence theorem cannot be used.