The triangles are congruent by the SSS congruence theorem.

Question

Triangles M N P and T S R are shown. Triangle M N P is shifted down and to the right and then is reflected across point P to form triangle T S R.

Which rigid transformation(s) can map TriangleMNP onto TriangleTSR?

reflection only
rotation only
translation, then reflection
translation, then rotation

Answer 1

To determine which rigid transformations can map Triangle MNP onto Triangle TSR based on your description, let's analyze the operations involved:

1. Translation: Triangle MNP is shifted down and to the right. This means that every point of triangle MNP moves to a new position, but the shape and size of the triangle remain unchanged.

2. Reflection: After the translation, triangle MNP is reflected across point P to form triangle TSR. This means that the triangle is flipped over point P, maintaining the congruence of the triangles as the corresponding sides and angles remain the same.

Given these transformations:

• Translation, then Reflection: This sequence accurately describes how Triangle MNP is transformed into Triangle TSR, first by translating the triangle to a new position and then reflecting it to end up in the final shape and orientation.

Thus, the correct answer is translation, then reflection.