What if you were presented with two angles that are on the same side of a transversal, but inside the lines? How would you describe these angles and what could you conclude about their measures? After completing this Concept, you'll be able to answer these questions using your knowledge of same side interior angles.
CK-12 Foundation: Chapter3SameSideInteriorAnglesA
Watch the portions of this video dealing with same side interior angles.
James Sousa: Angles and Transversals
James Sousa: Proof that Consecutive Interior Angles Are Supplementary
James Sousa: Proof of Consecutive Interior Angles Converse
Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.
Converse of the Same Side Interior Angles Theorem: If two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel.
Using the picture above, list all the pairs of same side interior angles.
This example shows why if two parallel lines are cut by a transversal, the same side interior angles are supplementary.
For questions 1-2, determine if each angle pair below is congruent, supplementary or neither.
∠5 and ∠8
∠2 and ∠3
- Are the lines below parallel? Justify your answer.
In 4-5, use the given information to determine which lines are parallel. If there are none, write none. Consider each question individually.
∠AFD and ∠BDF are supplementary
∠DIJ and ∠FJI are supplementary
m∠3=(3x+25)∘ and m∠5=(4x−55)∘
m∠4=(2x+15)∘ and m∠6=(3x−5)∘
m∠3=(x+17)∘ and m∠5=(3x−5)∘
m∠4=(3x+12)∘ and m∠6=(4x−1)∘
m∠3=(2x+14)∘ and m∠5=(3x−2)∘
m∠4=(5x+16)∘ and m∠6=(7x−4)∘
For 12-13, determine whether the statement is true or false.
- Same side interior angles are on the same side of the transversal.
- Same side interior angles are congruent when lines are parallel.
For questions 14-15, use the picture below.
- What is the same side interior angle with ∠3?
- Are the lines parallel? Explain.