Chapter 12.2, Problem 25E

To determine

To prove:

The criteria for congruent triangles is equivalent to the congruence in terms of rigid motion.

Explanation of Solution

Given:

The two triangle

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.

All the corresponding parts are congruent.

If all corresponding parts of two triangles are congruent.

The triangle are congruent.

A (rigid motion) maps each part of a figure to a corresponding part of image because (rigid motion) preserve length and angle measure corresponding parts of congruent figures are (congruent) that is corresponding sides and angles are congruent.