Question

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

Explanation:

Step1: Identify corresponding sides and angles

In $\triangle XYZ$ and $\triangle RST$, we have $XY = RS=5$ in, $YZ = ST = 12$ in, $XZ=RT = 14$ in and corresponding angles are equal as marked.

Step2: Recall the concept of rigid - motions

Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures. Since the corresponding side - lengths and angle - measures of $\triangle XYZ$ and $\triangle RST$ are equal, we can use a rigid motion to map one triangle onto the other. A reflection can be used to map $\triangle XYZ$ onto $\triangle RST$ because the orientation of the triangles is mirror - like.

Answer:

Yes. A reflection can map $\triangle XYZ$ onto $\triangle RST$.