Logical Proof Question?

Question

Given: -ray JK bisects GHJ
-angle ABC is congruent to angle GHK

Prove: angle ABC is congruent to angle KHJ

Answer 1

Bisect by definition means that the two angles GHK and KHJ have equivalent measures and are therefore congruent.

Since ABC is congruent to GHK and GHK is congruent to KHJ, then ABC is congruent to angle KHJ (transititive property)

Answer 2

Since ray JK bisects GHJ, it would split angle GHJ into 2 congruent angles. These 2 congruent angles are GHK and KHJ. Since the given tells that ABC is congruent to angle GHK. Then ABC would have to be congruent to angle KHJ because the ray bisected GHJ into congruent angles.