Consecutive Interior Angles Theorem
Consecutive Interior Angles
Consecutive Interior Angles are formed when two parallel lines are cut by a transversal.
In the figure, angles 3 and 5 are consecutive interior angles.
Also angles 4 and 6 are consecutive interior angles.
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary.
Proof:
Given: k || l is a transversal
Prove: 
are supplementary and 
are supplementary.
Statement |
Reason |
|
1 |
k || l, t is a traversal. |
Given |
2 |
 form a linear pair and  form a linear pair. |
Definition of linear pair |
3 |
are supplementary
are supplementary. |
Supplement postulate |
4 |
 |
Alternate Interior Angle Theorem |
5 |
are supplementary are supplementary. |
Substitution Property |
