Final answer:
In the congruence statement ARAT = AHOG, each letter corresponds to a side in the triangles being compared. The side AT in ARAT corresponds to the side OG in AHOG. Therefore, answer D, side length OG, is congruent to side length AT.
Step-by-step explanation:
When dealing with a congruence statement in geometry, like ARAT = AHOG, it's important to compare the corresponding parts of congruent figures. Each letter corresponds to a vertex of a triangle, which means that each pair of letters represents a side in the triangle. In the congruence statement provided, the side that corresponds to AT in ARAT would be the side that is in the same position in AHOG. The sides in the congruent figures are as follows: A corresponds to A, R to H, A to O, and T to G. Therefore, the side AT in ARAT corresponds to OG in AHOG.
So, the answer to the question is D. Side length OG is congruent to side length AT.