Question

5.
a. describe a transformation that could be used to show that corresponding angles are congruent.
b. describe a transformation that could be used to show that alternate interior angles are congruent.

Explanation:

Step1: Translation for corresponding angles

A translation (a slide) of line \( l \) to line \( m \) would map angle \( \angle BAD\) to \( \angle BDE\). Since translation is a rigid - motion (preserves shape and size), corresponding angles \( \angle BAD\) and \( \angle BDE\) are congruent.

Step2: Rotation for alternate - interior angles

A rotation of \( 180^{\circ}\) about the mid - point of segment \( AD\). Let \( O\) be the mid - point of \( AD\). A rotation \( R_{O,180^{\circ}}\) (rotation about point \( O\) by \( 180^{\circ}\)) maps \( \angle BAD\) to \( \angle ADE\). Since rotation is a rigid - motion (preserves shape and size), alternate - interior angles \( \angle BAD\) and \( \angle ADE\) are congruent.

Answer:

a. A translation of line \( l \) to line \( m \).
b. A \( 180^{\circ}\) rotation about the mid - point of the segment connecting a point on the transversal (e.g., segment \( AD\)).