Question

1. describe a rigid transformation that could be used to show that corresponding angles are congruent.

Explanation:

Step1: Recall the definition of translation

Translation is a type of rigid transformation that slides every point of a figure or space by the same distance in a given direction.

Step2: Apply translation concept

If we translate the line with angles \(1 - 4\) so that it coincides with the line with angles \(5 - 8\), the corresponding angles (e.g., \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\)) will overlap. Since translation preserves the measure of angles (as it is a rigid transformation), corresponding angles are congruent.

Answer:

A translation (a type of rigid transformation) can be used. Translate the line with angles \(1 - 4\) so that it maps onto the line with angles \(5 - 8\). Since translation preserves angle - measure, corresponding angles are congruent.