Question

the asa congruence theorem quick check. use the image to answer the question. to prove △abc≅△abc, which of the following shows how the asa criterion follows from the definition of congruence in terms of rigid motions? (1 point) rotate △abc 90 degrees (counter - clockwise) about vertex c, and then reflect △abc across (overline{ca}). rotate △abc - 90 degrees (clockwise) about vertex c, and then reflect △abc across (overline{ca}). rotate △abc 360 degrees (counter - clockwise), and then reflect △abc across (overline{bc}). rotate △abc - 90 degrees (clockwise) about vertex c, and then reflect △abc across (overline{bc}).

Explanation:

Step1: Analyze rigid - motions

Rigid motions include rotations and reflections.

Step2: Check rotation

A - 90 - degree (clockwise) rotation about $C$ aligns some parts.

Step3: Check reflection

Reflection across $\overline{CA'}$ after rotation can map $\triangle ABC$ to $\triangle A''B''C''$ to satisfy ASA congruence in terms of rigid - motions.

Answer:

Rotate $\triangle ABC$ - 90 degrees (clockwise) about vertex $C$, and then reflect $\triangle A'B'C'$ across $\overline{CA'}$