Question

is △abc congruent to △xyz? justify your answer using rigid motions.
yes. a translation and a reflection can map △abc onto △xyz.
yes. a translation and a dilation can map △abc onto △xyz.
no. it is not possible to map △abc onto △xyz using only rigid motions.

Explanation:

Step1: Recall rigid - motion definition

Rigid motions include translations, rotations, and reflections. They preserve side - lengths and angles.

Step2: Compare side - lengths

In $\triangle ABC$, sides are 9 in, 9 in, 13 in. In $\triangle XYZ$, sides are 12 in, 12 in, 13 in. Side - lengths are not equal.

Step3: Determine congruence

Since rigid motions preserve side - lengths and the side - lengths of $\triangle ABC$ and $\triangle XYZ$ are not equal, we cannot map $\triangle ABC$ onto $\triangle XYZ$ using only rigid motions.

Answer:

No. It is not possible to map $\triangle ABC$ onto $\triangle XYZ$ using only rigid motions.