Question

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

Explanation:

Step1: Recall rigid - motion definition

Rigid motions (translations, rotations, reflections) preserve side - lengths and angle - measures. If we can map one triangle onto another using rigid motions, the triangles are congruent.

Step2: Analyze the triangles

By observing the side - length markings (congruent sides) and angle - measure markings (congruent angles) on \(\triangle EFG\) and \(\triangle XYZ\), we can see that they have the same shape and size. A translation can first be used to move \(\triangle EFG\) so that one of its vertices coincides with a corresponding vertex of \(\triangle XYZ\). Then, a rotation can be used to align the sides and angles of the two triangles.

Answer:

Yes. A translation and a rotation can map \(\triangle EFG\) onto \(\triangle XYZ\).