Question

1. given: $overrightarrow{km}$ bisects $angle{jkl}$ prove: $mangle{mkl}=\frac{1}{2}mangle{jkl}$ statements reasons 1. $overrightarrow{km}$ bisects $angle{jkl}$ 1. givin 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

$\overrightarrow{KM}$ bisects $\angle{JKL}$ (Given)

Step2: Definition of angle - bisector

If a ray bisects an angle, it divides the angle into two congruent angles. So, $m\angle{JKM}=m\angle{MKL}$ (Definition of angle - bisector)

Step3: Angle - addition postulate

The sum of the measures of two adjacent angles with a common ray is equal to the measure of the larger angle. So, $m\angle{JKM}+m\angle{MKL}=m\angle{JKL}$ (Angle - addition postulate)

Step4: Substitution

Since $m\angle{JKM}=m\angle{MKL}$, we substitute $m\angle{JKM}$ with $m\angle{MKL}$ in the equation $m\angle{JKM}+m\angle{MKL}=m\angle{JKL}$, getting $m\angle{MKL}+m\angle{MKL}=m\angle{JKL}$ (Substitution property of equality)

Step5: Simplification

Combining like - terms, $m\angle{MKL}+m\angle{MKL}=2m\angle{MKL}$, so $2m\angle{MKL}=m\angle{JKL}$ (Simplification)

Step6: Division property of equality

Dividing both sides of the equation $2m\angle{MKL}=m\angle{JKL}$ by 2, we get $m\angle{MKL}=\frac{1}{2}m\angle{JKL}$ (Division property of equality)

Answer:

1. Given
2. Definition of angle - bisector
3. Angle - addition postulate
4. Substitution property of equality
5. Simplification
6. Division property of equality