Interior Angles Theorem Proof

Interior Angles Theorem: If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.

Given: Alternate Exterior Angles a b with transversal t

Statements/Conclusion Justification

1) a b with transversal t 1) Given

2) ray BA and ray BC are opposite rays. 2) Definition of opposite rays

3) ABC is a straight angle. 3) Straight Angle Assumption

4) mABC = 180 degrees. 4) Definition of straight angle

5) m1 + m4 = mABC 5) Angle Addition Assumption

6) m1 = m5 6) Parallel Lines Postulate

7) m5 + m4 = mABC 7) Substitution Property

8) m5 + m4 = 180 8) Substitution Property

9) 5 and 4 are supplementary. 9) Definition of supplementary angles

Statements/Conclusion	Justification
1) a b with transversal t	1) Given
2) and are opposite rays.	2) Definition of opposite rays
3) ABC is a straight angle.	3) Straight Angle Assumption
4) mABC = 180 degrees.	4) Definition of straight angle
5) m1 + m4 = mABC	5) Angle Addition Assumption
6) m1 = m5	6) Parallel Lines Postulate
7) m5 + m4 = mABC	7) Substitution Property
8) m5 + m4 = 180	8) Substitution Property
9) 5 and 4 are supplementary.	9) Definition of supplementary angles

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