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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.

Math diagram

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.


Given: k l , t is a transversal

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

k l , t is a traversal.
1 and 3 form a linear pair and 2 and 4 form a linear pair.
Definition of linear pair

1 and 3 are supplementary

m 1 + m 3 = 180 °

2 and 4 are supplementary

m 2 + m 4 = 180 °

1 5 and 2 6
Corresponding Angles Theorem
3 and 5 are supplementary 4 and 6 are supplementary.
Substitution Property




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