Question

1. consider triangles mnp and xyz.

which statement is true?
a triangle mnp is congruent to triangle xyz because there is a sequence of rotations, reflections, and/or translations that maps triangle mnp onto triangle xyz.
b triangle mnp is congruent to triangle xyz because there is no sequence of rotations, reflections, or translations that maps triangle mnp onto triangle xyz.
c triangle mnp is not congruent to triangle xyz because there is a sequence of rotations, reflections, and/or translations that maps triangle mnp onto triangle xyz.
d triangle mnp is not congruent to triangle xyz because there is no sequence of rotations, reflections, or translations that maps triangle mnp onto triangle xyz.

Explanation:

To determine congruence of triangles via rigid transformations (rotations, reflections, translations), we check if one can be mapped to the other. Congruent triangles can be mapped using such transformations.

• Option A: Correctly states that if a sequence of rigid transformations maps \( \triangle MNP \) to \( \triangle XYZ \), they are congruent.
• Option B: Contradicts the definition (no sequence would mean non - congruent, but this says they are congruent).
• Option C: Illogical (a mapping sequence implies congruence, but it says not congruent).
• Option D: If no sequence exists, they are non - congruent, but visually, the triangles appear to have the same shape and size (so a mapping sequence should exist, making D wrong).

Answer:

A. Triangle \( MNP \) is congruent to triangle \( XYZ \) because there is a sequence of rotations, reflections, and/or translations that maps triangle \( MNP \) onto triangle \( XYZ \).