Question

You are given two pairs of triangles. For the first pair of triangles, each angle and side of one triangle is congruent to the corresponding angle and side of the other. You show that rigid motions can transform one triangle so that it matches up with the other. For the second pair of triangles, you show that rigid motions can transform one triangle so that each side or angle of one triangle matches exactly with a corresponding side or angle of the other triangle. What have you proved?
a) If corresponding pairs of sides and corresponding pairs of angles of two triangles are congruent, then the triangles can be matched up exactly using rigid motions.

b) If two triangles can be matched up exactly using rigid motions, then corresponding pairs of sides and corresponding pairs of angles of the triangles are congruent.

c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

d) If corresponding pairs of sides and corresponding pairs of angles of two triangles are not congruent, then the triangles are not congruent.

Answer 1

Answer:

C

Step by step explanation:

When you move a shape via rigid transformations, the dimensions of the shape do not change (by definition). This includes translation and rotation. Since the size or measure of any of the side lengths or angles is not changing when you move the shape, the only way that you can match one shape onto another with rigid transformations is if all of the corresponding sides and angles are congruent. Therefore, the correct answer is choice C. Hope this helps!