Question

parallelogram defg has been rotated.
which statements are correct? check all that apply.
□ point f → point f
□ parallelogram defg → parallelogram gfed
□ point d of the pre - image corresponds to point d of the image.
□ \\(\overline{ed}\\) of the pre - image corresponds to \\(\overline{gf}\\) of the image.
□ parallelogram defg maps to parallelogram defg.

Explanation:

1. point F → point F': Rotation maps each pre-image point to a unique image point, not the same point, so this is incorrect.
2. parallelogram DEFG → parallelogram G'F'E'D': Match congruent sides/angles: pre-image DEFG (sides: GF, FE, ED, DG; angles at G, F, E, D) maps to image G'F'E'D' (sides: D'E', E'F', F'G', G'D'; angles at D', E', F', G'). The congruence marks confirm this correspondence, so this is correct.
3. Point D of the pre-image corresponds to point D' of the image: The angle mark at pre-image D matches the angle mark at image D', so this correspondence is correct.
4. $\overline{ED}$ of the pre-image corresponds to $\overline{G'F'}$ of the image: Pre-image $\overline{ED}$ has double hash marks; image $\overline{G'F'}$ has single hash marks. Congruent sides (matching hashes) are the corresponding sides, so this is incorrect.
5. Parallelogram DEFG maps to parallelogram D'E'F'G': This order does not match the congruent side/angle correspondences shown, so this is incorrect.

Answer:

• parallelogram DEFG → parallelogram G'F'E'D'
• Point D of the pre-image corresponds to point D' of the image.