Final answer:
The Angle-Angle Theorem verifies that HIJ = MLN.
Step-by-step explanation:
The theorem that verifies that HIJ = MLN is the Angle-Angle Theorem. The Angle-Angle Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, since angle H is congruent to angle M and angle J is congruent to angle N, we can conclude that triangles HIJ and MLN are similar and therefore their corresponding sides are proportional.