Exercise 15 Page 623

From the given information, we know two sides of the triangles are congruent. Additionally, note that △ LMJ and △ JKL both share JL as a side so in addition to the given information, we can say by the Reflexive Property of Congruence that the side JL is congruent to itself.

When we know that all corresponding sides are congruent, we can by the SSS Congruence Theorem claim that △ LMJ ≅ △ JKL.

Alternative Solution

Two-Column Proof

Let's write this as a two-column proof.

Statement	Reason
1. &LM≅ JK, MJ⊥ KL	1. Given
2. JL ≅ JL	2. Reflexive Property of Congruence
3. △ LMJ ≅ △ JKL	3. SSS Congruence Theorem