Question

triangle abc is congruent to triangle abc. describe a sequence of rigid motions that takes a to a, b to b, and c to c.

Explanation:

Step1: Translate point A to A'

Move triangle ABC so that point A coincides with A'.

Step2: Rotate the triangle

Rotate the translated - triangle around A' so that one of the sides (say AB) aligns with the corresponding side (A'B') of triangle A'B'C'.

Step3: Reflect (if necessary)

Check if the triangles are fully congruent. If not, a reflection may be required to make all vertices match. In this case, after translation and rotation, if the orientation is still not correct, reflect the triangle across an appropriate line to make B match B' and C match C'.

Answer:

First, translate triangle ABC so that point A coincides with A'. Then, rotate the translated triangle around A' to align one side with the corresponding side of triangle A'B'C'. If needed, reflect the triangle across a line to make all vertices match.