Question

1. given: \\(\overrightarrow{km}\\) bisects \\(\angle jkl\\)

prove: \\( m\angle mkl = \frac{1}{2}m\angle jkl \\)

statements	reasons
2. \\( m\angle jkm = m\angle mkl \\)	2.
3. \\( m\angle jkm + m\angle mkl = m\angle jkl \\)	3.
4. \\( m\angle mkl + m\angle mkl = m\angle jkl \\)	4.
5. \\( 2m\angle mkl = m\angle jkl \\)	5.
6. \\( m\angle mkl = \frac{1}{2}m\angle jkl \\)	6.

Explanation:

Step1: Identify Reason for Statement 1

The first statement is given, so the reason is "Given".

Step2: Identify Reason for Statement 2

By the definition of an angle bisector, it divides the angle into two equal - measure angles. So the reason is "Definition of Angle Bisector".

Step3: Identify Reason for Statement 3

This is based on the Angle Addition Postulate, which states that if a point lies in the interior of an angle, the sum of the measures of the two adjacent angles formed is equal to the measure of the original angle. So the reason is "Angle Addition Postulate".

Step4: Identify Reason for Statement 4

We substitute \(m\angle JKM\) with \(m\angle MKL\) (from Statement 2), so the reason is "Substitution Property of Equality".

Step5: Identify Reason for Statement 5

Combining like terms (\(m\angle MKL + m\angle MKL=2m\angle MKL\)), so the reason is "Combining Like Terms".

Step6: Identify Reason for Statement 6

We divide both sides of the equation \(2m\angle MKL = m\angle JKL\) by 2, which is the "Division Property of Equality".

Answer:

1. Given
2. Definition of Angle Bisector
3. Angle Addition Postulate
4. Substitution Property of Equality
5. Combining Like Terms
6. Division Property of Equality