Question

What additional information do you need to prove that ∆AMD ≅ ∆CNB by the HL Theorem?

Answer 1

(H)ypotenuse (L)eg, right-triangle theorem.

based on the provided graph, we know the hypotenuses are equal, thus the tickmarks, so H is true, now the L part, we only need either of the pair of legs to be equal DM = NB or AM = CN, if either one is true, we're golden.