PLEASE Use rigid motion to prove that figure ABC is congruent to figure EFG

a) Translate ABC using directed line segment AE. Rotate A'B'C' using E as the center until C' coincides with G.

Step-by-step explanation:

If we consider ABC figure as a rigid body, then we can translate it to any point in space, keeping the lengths and directions of its elements same. So, to prove congruency of two figures we will try to make them coincident on each other. So, first we translate the figure ABC, along a straight line projected from A to E, such that point A meets Point E. We call this repositioned figure A'B'C' Now, another property of rigid body is that it can rotate as a whole body about any of its internal points.

Since, A' and E are coincident now so, we rotate figure A'B'C', with A' as the center of rotation. This rotation is anti-clockwise and we rotate it until C' coincides with G. Now, both figures are coincident. Hence, their congruency is proven.

Therefore, the correct answer is:

a) Translate ABC using directed line segment AE. Rotate A'B'C' using E as the center until C' coincides with G.