Final answer:
To prove triangle HGJ is congruent to triangle MLK, we need to show that all corresponding angles and sides are equal. Additional information A, B, and C are sufficient, but additional information D is not sufficient.
Step-by-step explanation:
To prove that triangle HGJ is congruent to triangle MLK, we need to show that all corresponding angles and sides are equal.
A) The measure of angle H is equal to the measure of angle M: This is a piece of sufficient additional information because corresponding angles are congruent in congruent triangles.
B) The measure of angle G is equal to the measure of angle L: This is a piece of sufficient additional information because corresponding angles are congruent in congruent triangles.
C) The measure of side HG is equal to the measure of side ML: This is a piece of sufficient additional information because corresponding sides are congruent in congruent triangles.
D) The measure of side HJ is equal to the measure of side LK: This is not a piece of sufficient additional information because the sides must be in the same order in both triangles for congruence.
Therefore, option D is not sufficient additional information to prove triangle HGJ is congruent to triangle MLK.