Exercise 18 Page 631

Using the Segment Addition Postulate, we can write the following two equations describing the length of AK and CJ: AK&=AJ+JK CJ&=KC+JK By the Reflexive Property of Congruence we know that JK ≅ JK. Additionally, the given information, AJ ≅ KC, allows us to, by the Substitution Property of Congruence, rewrite one of the equations: AK&= KC+JK CJ&=KC+JK Finally, using the Transitive Property of Equality we can show that AK=CJ. Thus, by the definition of congruence AK≅ CJ. Let's separate △ ABK and △ CBJ and add the information we have found.

Now we have enough information to prove congruence using the ASA Congruence Theorem.