Match the reasons with the statements given.
given:
abr
| |
1 = 2
prove:
ra = rb

1. , :  Given

2. : If lines ||, corresponding  are =.

3. : If lines ||, alternate interior are =.

4. : Substitution.

5. : If two of a triangle are =, sides opposite are =.

Step-by-step explanation:

We have been given a two column proof and we are asked to match the correct reason with each statement.

We have been given that line segment RS is parallel to line segment AB and measure of angle 1 is equal to measure of angle 2.

1. , :  Given

We know corresponding angles of two parallel lines are equal, therefore, measure of angle B is equal to measure of angle 1.

2. : If lines ||, corresponding  are =.

We know that alternate interior angles of two parallel lines are equal. We can see that angle A and angle 2 are alternate interior angles of parallel lines RS and AB, therefore, measure of angle A is equal to measure of angle 2.

3. : If lines ||, alternate interior are =.

We have been given that . We figured that and . By substitution property of equality .

4. : Substitution.

We know that if two angles of a triangle are equal, then the sides opposite to these angles are also equal. We can see that side RA is opposite side of angle B and side RB is opposite side of angle A.

Since , then side .

5. : If two of a triangle are =, sides opposite are =.