Question

GIVEN:MN is an angle bisector of ∠JMK
Prove:m∠JMN=1/2m∠JMK

Answer 1

Explanation:

Statements Reasons

1. MN is an angle bisector of ∠JMK 1. Given

2. ∠JMN ≅ ∠NMK 2. Definition of an angle bisector

3. m∠JMN ≅ m∠NMK 3. Definition of congruent angles

4. m∠JMN + m∠NMK = m∠JMK 4. Angle addition postulate

5. m∠JMN + m∠JMN = m∠JMK 5. Substitution property

6. 2(m∠JMN) = m∠JMK 6. Addition property of equality

7. m∠JMN =
`(1)/(2)(m\angle JMK)` 7. Division property of equality