Question

how do we know that a triangle and its transformed image are congruent?

Explanation:

Congruent triangles have equal corresponding sides and angles. Transformations like translation (sliding), rotation (turning), and reflection (flipping) preserve side lengths and angle measures. So, if a triangle is transformed using these rigid motions, the original and transformed triangle are congruent.

Answer:

A triangle and its transformed image are congruent if the transformation is a rigid motion (translation, rotation, or reflection) because these transformations preserve side - lengths and angle measures.