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: kl , t is a transversal

Prove: 3 and 5 are supplementary and 4 and 6 are supplementary.

 
Statement
Reason
1
kl , t is a traversal.
Given
2
1 and 3 form a linear pair and 2 and 4 form a linear pair.
Definition of linear pair
3

1 and 3 are supplementary

m1+m3=180°

2 and 4 are supplementary

m2+m4=180°

4
15 and 26
Corresponding Angles Theorem
5
3 and 5 are supplementary 4 and 6 are supplementary.
Substitution Property