Download Same Side Interior Angles

Same Side Interior Angles
Bill Zahner
Lori Jordan
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Printed: May 5, 2016
AUTHORS
Bill Zahner
Lori Jordan
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 their relationship with parallel lines.
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.
Watch This
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/136891
CK-12 Foundation: Chapter3SameSideInteriorAnglesA
Watch the portions of this video dealing with same side interior angles.
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/1328
James Sousa: Angles and Transversals
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/1334
James Sousa: Proof that Consecutive Interior Angles Are Supplementary
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/1335
James Sousa: Proof of Consecutive Interior Angles Converse
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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. 6 3 and 6 5 are same side interior angles.
Same Side Interior Angles Theorem: If two parallel lines are cut by a transversal, then the same side interior
angles are supplementary.
So, if l || m and both are cut by t, then m6 3 + m6 5 = 180◦ and m6 4 + m6 6 = 180◦ .
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.
Example A
Using the picture above, list all the pairs of same side interior angles.
Same Side Interior Angles: 6 4 and 6 6, 6 5 and 6 3.
Example B
Find m6 2.
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Chapter 1. Same Side Interior Angles
Here, m6 1 = 66◦ because they are alternate interior angles. 6 1 and 6 2 are a linear pair, so they are supplementary.
m6 1 + m6 2 = 180◦
66◦ + m6 2 = 180◦
m6 2 = 114◦
This example shows why if two parallel lines are cut by a transversal, the same side interior angles are supplementary.
Example C
Find the measure of x.
The given angles are same side interior angles. The lines are parallel, therefore the angles add up to 180◦ . Write an
equation.
(2x + 43)◦ + (2x − 3)◦ = 180◦
(4x + 40)◦ = 180◦
4x = 140◦
x = 35◦
Watch this video for help with the Examples above.
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MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/136892
CK-12 Foundation: Chapter3SameSideInteriorAnglesB
Guided Practice
1. Is l || m? How do you know?
2. Find the value of x.
3. Find the value of x if m6 3 = (3x + 12)◦ and m6 5 = (5x + 8)◦ .
Answers:
1. These are Same Side Interior Angles. So, if they add up to 180◦ , then l || m. 113◦ + 67◦ = 180◦ , therefore l || m.
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Chapter 1. Same Side Interior Angles
2. 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
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
Interactive Practice
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/113010
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.
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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
For 6-11, what does the value of x have to be to make the lines parallel?
6.
7.
8.
9.
10.
11.
m6
m6
m6
m6
m6
m6
3 = (3x + 25)◦ and m6 5 = (4x − 55)◦
4 = (2x + 15)◦ and m6 6 = (3x − 5)◦
3 = (x + 17)◦ and m6 5 = (3x − 5)◦
4 = (3x + 12)◦ and m6 6 = (4x − 1)◦
3 = (2x + 14)◦ and m6 5 = (3x − 2)◦
4 = (5x + 16)◦ and m6 6 = (7x − 4)◦
For 12-13, determine whether the statement is true or false.
12. Same side interior angles are on the same side of the transversal.
13. Same side interior angles are congruent when lines are parallel.
For questions 14-15, use the picture below.
14. What is the same side interior angle with 6 3?
15. Are the lines parallel? Explain.
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Chapter 1. Same Side Interior Angles
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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