Question

a rotation by angle ∠ace using point c as the center takes triangle cba onto triangle cde.
a. explain why the image of ray ca lines up with ray ce.

Explanation:

The rotation is defined with center \( C \) and angle \( \angle ACE \). By the definition of a rotation about a center, the angle between a pre-image ray from the center and its image ray equals the rotation angle. Here, the rotation angle is \( \angle ACE \), so ray \( CA \) (from the center \( C \)) must map to the ray that forms \( \angle ACE \) with \( CA \), which is ray \( CE \).

Answer:

The rotation has center \( C \) and angle \( \angle ACE \). By rotation definition, the image of ray \( CA \) must form the rotation angle with \( CA \) from center \( C \), so it aligns with ray \( CE \).