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 (isometries) include translations, rotations, and reflections which preserve side - lengths and angle - measures.

Step2: Analyze congruence by rigid motions

If we can map one triangle onto another using a sequence of rigid motions, the triangles are congruent. By observing the orientation and position of \(\triangle EFG\) and \(\triangle XYZ\), we can first translate \(\triangle EFG\) so that one of its vertices coincides with a corresponding vertex of \(\triangle XYZ\). Then, we can rotate \(\triangle EFG\) to align the sides and angles.

Answer:

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