Question

1. given: $overline{km}$ bisects $angle{jkl}$

prove: $mangle{mkl}=\frac{1}{2}mangle{jkl}$

statements	reasons
2. $mangle{jkm}=mangle{mkl}$	2.
3. $mangle{jkm}+mangle{mkl}=mangle{jkl}$	3.
4. $mangle{mkl}+mangle{mkl}=mangle{jkl}$	4.
5. $2mangle{mkl}=mangle{jkl}$	5.
6. $mangle{mkl}=\frac{1}{2}mangle{jkl}$	6.

Explanation:

Step1: Given information

Given

Step2: Definition of angle - bisector

Definition of angle - bisector

Step3: Angle - addition postulate

Angle - addition postulate

Step4: Substitution property

Substitute \(m\angle JKM\) with \(m\angle MKL\)

Step5: Simplify the left - hand side

Combining like terms

Step6: Division property of equality

Divide both sides by 2

Answer:

Statements	Reasons
2. \(m\angle JKM=m\angle MKL\)	2. Definition of angle - bisector
3. \(m\angle JKM + m\angle MKL=m\angle JKL\)	3. Angle - addition postulate
4. \(m\angle MKL + m\angle MKL=m\angle JKL\)	4. Substitution property
5. \(2m\angle MKL=m\angle JKL\)	5. Combining like terms
6. \(m\angle MKL=\frac{1}{2}m\angle JKL\)	6. Division property of equality