Same Side Interior Angles
Dan Greenberg
Lori Jordan
Andrew Gloag
Victor Cifarelli
Jim Sconyers
Bill Zahner
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Printed: November 7, 2015
AUTHORS
Dan Greenberg
Lori Jordan
Andrew Gloag
Victor Cifarelli
Jim Sconyers
Bill Zahner
www.ck12.org
C HAPTER
Chapter 1. Same Side Interior Angles
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Same Side Interior Angles
Here you’ll learn what same side interior angles are and what relationship they have with parallel lines.
What if you were presented with two angles that are on the same side of the transversal and on the interior of
the two 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 and apply same side interior angle theorems to
find the measure of unknown angles.
Watch This
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CK-12 Same Side Interior Angles
Watch the portions of this video dealing with same side interior angles.
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James Sousa: Angles and Transversals
Then watch this video.
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James Sousa: Proof that Consecutive Interior Angles Are Supplementary
Finally, watch this video.
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James Sousa: Proof of Consecutive Interior Angles Converse
Guidance
Same side interior angles are two angles that are on the same side of the transversal and on the interior of the two
lines.
Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior
angles are supplementary.
If l||m, then m6 1 + m6 2 = 180◦ .
Converse of the Same Side Interior Angles Theorem: If two lines are cut by a transversal and the same side
interior angles are supplementary, then the lines are parallel.
If
then l||m.
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Chapter 1. Same Side Interior Angles
Example A
Find z.
z + 116◦ = 180◦ so z = 64◦ by Same Side Interior Angles Theorem.
Example B
Is l||m? How do you know?
These angles are Same Side Interior Angles. So, if they add up to 180◦ , then l||m.
130◦ + 67◦ = 197◦ , therefore the lines are not parallel.
Example C
Give two examples of same side interior angles in the diagram below:
There are MANY examples of same side interior angles in the diagram. Two are 6 6 and 6 10, and 6 8 and 6 12.
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CK-12 Same Side Interior Angles
–>
Guided Practice
1. Find the value of x.
2. Find the value of y.
3. Find the value of x if m6 3 = (3x + 12)◦ and m6 5 = (5x + 8)◦ .
Answers:
1. The given angles are same side interior angles. Because the lines are parallel, the angles add up to 180◦ .
(2x + 43)◦ + (2x − 3)◦ = 180◦
(4x + 40)◦ = 180◦
4x = 140
x = 35
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Chapter 1. Same Side Interior Angles
2. y is a same side interior angle with the marked right angle. This means that 90◦ + y = 180 so y = 90.
3. These are same side interior angles so set up an equation and solve for x. Remember that same side interior angles
add up to 180◦ .
(3x + 12)◦ + (5x + 8)◦ = 180◦
(8x + 20)◦ = 180◦
8x = 160
x = 20
Explore More
For questions 1-2, determine if each angle pair below is congruent, supplementary or neither.
1. 6 5 and 6 8
2. 6 2 and 6 3
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.
4.
5.
6
6
AFD and 6 BDF are supplementary
DIJ and 6 FJI are supplementary
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For 6-8, what does the value of x have to be to make the lines parallel?
6. m6 3 = (3x + 25)◦ and m6 5 = (4x − 55)◦
7. m6 4 = (2x + 15)◦ and m6 6 = (3x − 5)◦
8. m6 3 = (x + 17)◦ and m6 5 = (3x − 5)◦
For 9-10, determine whether the statement is true or false.
9. Same side interior angles are on the same side of the transversal.
10. Same side interior angles are congruent when lines are parallel.
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 3.6.
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