The triangles above are right triangles and they have one pair of congruent legs. Therefore, to prove triangle congruence by the HL Congruence Theorem, we need the hypotenuses to be congruent. This means that we need LM ≅ LM.
b If K is the midpoint of JM, by definition of midpoint we have that JK = MK. Therefore, we have that JK ≅ MK. Moreover, by the Reflexive Property of Equality, we know that LK ≅ LK.
Since ∠ LKJ and ∠ LKM are both right angles, they are congruent by the Right Angles Congruence Theorem. Therefore, the triangles above have two pairs of congruent sides and a pair of congruent included angles. With this information, we can say that △ LKJ ≅ △ LKM by the SAS Congruence Theorem.
