Question

You are given two pairs of triangles.

For the first pair of triangles, each side and angle of one triangle is congruent to the corresponding side and angle 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 angle or side of one triangle matches exactly with a corresponding angle or side of the other triangle.

What have you proved?

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

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

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

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