Question

determine if the two figures are congruent and explain your answer using transformations.

Explanation:

Step1: Recall congruence and transformation rules

Two figures are congruent if one can be mapped onto the other through a sequence of rigid - motions (translations, rotations, and reflections). Rigid motions preserve side - lengths and angles.

Step2: Analyze possible transformations

We can try to find a sequence of translations, rotations, and reflections that map one figure to the other. First, we can observe the orientation and position of the two figures. If we rotate the lower figure 180 degrees about a point (say the origin if it is convenient in the coordinate system), and then translate it, we can see that the corresponding sides and angles of the two figures will match up.
Since we can map one figure onto the other through a sequence of rigid motions (a rotation and a translation), the two figures are congruent.

Answer:

The two figures are congruent because we can map one figure onto the other using a sequence of rigid motions (a rotation and a translation).