Consecutive Interior Angles Theorem

Statement

Reason

1

$k\parallel l$ , $t$ is a traversal.

Given

2

$\angle 1$ and $\angle 3$ form a linear pair and $\angle 2$ and $\angle 4$ form a linear pair.

Definition of linear pair

3

$\angle 1$ and $\angle 3$ are supplementary

$m\angle 1+m\angle 3=180°$

$\angle 2$ and $\angle 4$ are supplementary

$m\angle 2+m\angle 4=180°$

Supplement Postulate

4

$\angle 1\cong \angle 5$ and $\angle 2\cong \angle 6$

Corresponding Angles Theorem

5

$\angle 3$ and $\angle 5$ are supplementary $\angle 4$ and $\angle 6$ are supplementary.

Substitution Property