Chapter 12.2, Problem 18E

To determine

To describe:

The given triangle $\Delta MNP\cong \Delta RSP$ .

Explanation of Solution

Given:

  $\Delta MNP\cong \Delta RSP$

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.

The pairs of congruent corresponding angles

  $\begin{array}{l}\angle M=\angle R\\ \angle N=\angle S\end{array}$

Therefore,

The corresponding sides are not congruent.

So, it is wrong to conclude that $\Delta MNP\cong \Delta RSP$ only on that fact corresponding angles are congruent.