Given: IK bisects ∠HKJ, HK = JK
Prove: IK bisects ∠LHIJ
Proof:
Statement Reason
1. IK bisects ∠HKJ Given
2. HK = JK Given
3. ∠HKJ = ∠HKJ Reflexive property of equality
4. ∠HKJ = ∠JKH Definition of angle bisector
5. ∠HKJ + ∠JKH = 180° Angle sum property of a triangle
6. ∠HKJ + ∠HKJ = 180° Substitution (from statement 4)
7. 2∠HKJ = 180° Simplification (combining like terms)
8. ∠HKJ = 90° Division property of equality
9. ∠LHIJ = ∠HKJ Vertical angles are congruent
10. ∠LHIJ = 90° Substitution (from statement 8)
11. IK bisects ∠LHIJ Definition of angle bisector