Question

the triangles are congruent by the sss congruence theorem. which rigid transformation(s) can map △mnp onto △tsr? reflection only rotation only translation, then reflection translation, then rotation

Explanation:

Step1: Analyze the position of triangles

First, we can see that \(\triangle MNP\) and \(\triangle TSR\) are not in the same orientation. A translation (a slide) can be used to move \(\triangle MNP\) so that one of its vertices is in the same position - like moving \(M\) towards \(T\) (since \(MR = 7\) and \(TI=7\)).

Step2: Analyze the orientation after translation

After translation, we need to adjust the orientation. A reflection (a flip) can be used to make the triangles match exactly. For example, if we translate \(\triangle MNP\) so that \(MP\) is parallel to \(TI\) (after translation), then a reflection can be used to make the other sides and vertices match.

Answer:

translation, then reflection