Question

A student is trying to establish that alternate exterior angles are congruent using a transformational approach. They perform two isometric transformations to accomplish this. Using this diagram, determine the two isometric transformations, and EXPLAIN why this demonstrates that alternate exterior angles are congruent.

a) Translation and reflection; This demonstrates congruence by preserving distance and angles.
b) Rotation and dilation; This demonstrates congruence by changing the size and position of angles.
c) Reflection and dilation; This demonstrates congruence by reflecting and resizing angles.
d) Translation and rotation; This demonstrates congruence by changing the position and angle measure.

Answer 1

The two isometric transformations that demonstrate that alternate exterior angles are congruent are translation and reflection.

Step-by-step explanation:

The two isometric transformations that demonstrate that alternate exterior angles are congruent are translation and reflection.

Translation preserves distance and angles, so it does not change the measure of the alternate exterior angles. Reflection also preserves angles, so it does not change the measure of the alternate exterior angles either.

Therefore, using translation and reflection as isometric transformations, we can demonstrate that alternate exterior angles are congruent.