To prove triangle AB C cong triangle A^ prime prime B^ prime prime C^ prime prime which of the following shows how the ASA criterion follows from the definition of congruence in terms of rigid motions? (1 point) Rotate triangle ABC 90 degrees (counterclockwise) about vertex C, and then reflect triangle A' * B' * C' across overline C * A' . C Rotate triangle ABC - 90 degrees (clockwise) about vertex C, and then reflect triangle A' * B' * C' across overline B' * C . Rotate triangle ABC - 90 degrees (clockwise) about vertex C, and then reflect triangle A' * B' * C' across overline C * A' . Rotate triangle ABC 360 degrees (counterclockwise), and then reflect triangle A' * B' * C' across overline B' * C

Answer 1

To demonstrate that triangle \( ABC \) is congruent to triangle \( A''B''C'' \) using the ASA (Angle-Side-Angle) criterion and the definition of congruence in terms of rigid motions (which are rotations, reflections, and translations), we need to show that we can transform triangle \( ABC \) into triangle \( A''B''C'' \) using such motions.

Since the ASA criterion involves showing that two angles and the side between them are congruent, we can rotate and reflect the triangles to align them in such a way that these conditions are met.

Among the options provided, the correct interpretation would involve first aligning the triangles using rotation, then applying a reflection over the required side to make the two triangles coincide.

The option that seems most appropriate based on the ASA criterion would be:

• Rotate triangle ABC \( -90 \) degrees (clockwise) about vertex \( C \), and then reflect triangle \( A'B'C' \) across overline \( B'C' \).

This option suggests a rotation that would change the position of the triangle while maintaining its angles and side lengths, followed by a reflection to align the second triangle with the first.

Thus, we would be using rigid motions (rotation and reflection) to show that triangle \( ABC \) is congruent to triangle \( A''B''C'' \) through the ASA criterion.