The answer is C: Yes. One rigid motion is a translation of ABCD that maps point A to point D.
ABCD and DCFE are both quadrilaterals.
Given information:
ml || n (lines m and n are parallel)
pl || q (lines p and q are parallel)
D is the midpoint of BG
We need to determine if ABCD is congruent to DCFE and if there is a sequence of rigid motions that maps ABCD to DCFE.
Analysis:
Since ml || n and pl || q, and D is the midpoint of BG, we can see that ABCD and DCFE are parallelograms. This is because opposite sides of a parallelogram are parallel.
In parallelograms, opposite sides are congruent. Therefore, we have:
AB = DE
BC = EF
AD = CF
Additionally, since D is the midpoint of BG, we have:
BD = DG
Now, let's consider the rigid motions:
Translation: A translation moves an object without changing its orientation or size. In this case, we can translate ABCD by moving it to the right until point A coincides with point D. This will make ABCD congruent to DCFE.
Therefore, the answer is C. Yes. One rigid motion is a translation of ABCD that maps point A to point D.
The other options are not valid because:
A: This describes a composition of two rigid motions, which is not necessary in this case.
B: A 180° rotation would not map ABCD to DCFE because it would flip the figure, but the sides would not match.
D: As we have shown, there is a rigid motion (translation) that maps ABCD to DCFE.
Therefore, the answer is C. Yes. One rigid motion is a translation of ABCD that maps point A to point D.