Question

1. developing proof supply the missing reasons in the two - column proof. given: a||b, c||d prove: ∠1≅∠3 statements reasons 1) a||b 1) given 2) ∠3 and ∠2 are supplementary. 2) a. ? 3) c||d 3) given 4) ∠1 and ∠2 are supplementary. 4) b. ? 5) ∠1≅∠3 5) c. ?

Explanation:

Step1: Identify reason for statement 2

Since $c\parallel d$, same - side interior angles are supplementary. So the reason for $\angle3$ and $\angle2$ being supplementary is that same - side interior angles of parallel lines are supplementary.

Step2: Identify reason for statement 4

Since $a\parallel b$, same - side interior angles are supplementary. So the reason for $\angle1$ and $\angle2$ being supplementary is that same - side interior angles of parallel lines are supplementary.

Step3: Identify reason for statement 5

If two angles are supplementary to the same angle, then they are congruent. $\angle1$ and $\angle3$ are both supplementary to $\angle2$, so $\angle1\cong\angle3$ by the congruent supplements theorem.

Answer:

a. Same - side interior angles of parallel lines are supplementary.
b. Same - side interior angles of parallel lines are supplementary.
c. Congruent supplements theorem.