Consecutive Interior Angles Theorem

Consecutive Interior Angles

When two lines are cut by a transversal, the pair of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.

In the figure, the angles 3 and 5 are consecutive interior angles.

Also the 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

4
Corresponding Angles Theorem
5
are supplementary are supplementary.
Substitution Property