Question

Match the reasons with the statements given.

Answer 1

Answer:

1st corresponds to the 4th

2nd corresponds to the 1st

3rd corresponds to the 3rd

4th corresponds to the 2nd

5th corresponds to the 5th

Step-by-step explanation:

Answer 2

Answer:

1. $\overline{RS}||\overline{AB}$, $\angle 1=\angle 2$:  Given

2. $\angle B=\angle 1$: If lines ||, corresponding $\angle 's$  are =.

3. $\angle A=\angle 2$: If lines ||, alternate interior $\angle 's$ are =.

4. $\angle A=\angle B$: Substitution.

5. $RB=RA$: If two $\angle 's$ 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. $\overline{RS}||\overline{AB}$, $\angle 1=\angle 2$:  Given

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

2. $\angle B=\angle 1$: If lines ||, corresponding $\angle 's$  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. $\angle A=\angle 2$: If lines ||, alternate interior $\angle 's$ are =.

We have been given that $\angle 1=\angle 2$. We figured that $\angle A=\angle 2$ and $\angle B=\angle 1$. By substitution property of equality $\angle A=\angle B$.

4. $\angle A=\angle B$: 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 $\angle A=\angle B$, then side $RB=RA$.

5. $RB=RA$: If two $\angle 's$ of a triangle are =, sides opposite are =.