Question

What is the reason for Statement 3 of the two-column proof?

Answer 1

Refer to the attached image.

Given:

The measure of $\angle JMK= 52^\circ$ and $\angle KML= 38^\circ$.

Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove: $\angle JML$ is a right angle.

Proof:

  Statements                                                                                 Reasons

1. $m \angle JMK=52^\circ$                                            Given

2. $m \angle KML=38^\circ$                                           Given

3. $m \angle JMK+m \angle KML=m \angle JML$  

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. $52^\circ+38^\circ = m \angle JML$   Substitution property of equality

5. $90^\circ = m \angle JML$                  Simplification

6. $\angle$JML is a right angle.      Definition of right angle