Corresponding Angles
Dan Greenberg
Lori Jordan
Andrew Gloag
Victor Cifarelli
Jim Sconyers
Bill Zahner
Kimberly Hopkins
Jen Kershaw
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Printed: November 7, 2015
AUTHORS
Dan Greenberg
Lori Jordan
Andrew Gloag
Victor Cifarelli
Jim Sconyers
Bill Zahner
Kimberly Hopkins
Jen Kershaw
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C HAPTER
Chapter 1. Corresponding Angles
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Corresponding Angles
Here you’ll learn what corresponding angles are and what relationship they have with parallel lines.
What if you were presented with two angles that are in the same place with respect to the transversal but on different
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 use corresponding angle postulates.
Watch This
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/136571
CK-12 Corresponding Angles
Watch the portions of this video dealing with corresponding angles.
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/1328
James Sousa: Angles and Transversals
Then watch this video beginning at the 4:50 mark.
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/1331
James Sousa: Corresponding Angles Postulate
Finally, watch this video.
MEDIA
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URL: http://www.ck12.org/flx/render/embeddedobject/1332
1
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James Sousa: Corresponding Angles Converse
Guidance
Corresponding angles are two angles that are in the "same place" with respect to the transversal but on different
lines. Imagine sliding the four angles formed with line l down to line m. The angles which match up are corresponding.
Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the corresponding angles are
congruent.
If l||m, then 6 1 ∼
= 6 2.
Converse of Corresponding Angles Postulate: If corresponding angles are congruent when two lines are cut by a
transversal, then the lines are parallel.
If
then l||m.
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Chapter 1. Corresponding Angles
Example A
If a||b, which pairs of angles are congruent by the Corresponding Angles Postulate?
There are 4 pairs of congruent corresponding angles:
∼ 6 5, 6 2 ∼
6 1=
= 6 6, 6 3 ∼
= 6 7, and 6 4 ∼
= 6 8.
Example B
If m6 2 = 76◦ , what is m6 6?
2 and 6 6 are corresponding angles and l||m from the arrows in the figure. 6 2 ∼
= 6 6 by the Corresponding Angles
◦
Postulate, which means that m6 6 = 76 .
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Example C
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If m6 8 = 110◦ and m6 4 = 110◦ , then what do we know about lines l and m?
8 and 6 4 are corresponding angles. Since m6 8 = m6 4, we can conclude that l||m.
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CK-12 Corresponding Angles
–>
Guided Practice
1. Using the measures of 6 2 and 6 6 from Example B, find all the other angle measures.
2. Is l||m?
3. Find the value of y:
Answers:
1. If m6 2 = 76◦ , then m6 1 = 180◦ − 76◦ = 104◦ (linear pair). 6 3 ∼
= 6 2 (vertical angles), so m6 3 = 76◦ . m6 4 = 104◦
(vertical angle with 6 1).
By the Corresponding Angles Postulate, we know 6 1 ∼
= 6 5, 6 2 ∼
= 6 6, 6 3 ∼
= 6 7, and 6 4 ∼
= 6 8, so m6 5 = 104◦ , m6 6 =
76◦ , m6 7 = 76◦ , and m6 104◦ .
2. The two angles are corresponding and must be equal to say that l||m. 116◦ 6= 118◦ , so l is not parallel to m.
3. The horizontal lines are marked parallel and the angle marked 2y is corresponding to the angle marked 80 so these
two angles are congruent. This means that 2y = 80 and therefore y = 40.
Explore More
1. Determine if the angle pair 6 4 and 6 2 is congruent, supplementary or neither:
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Chapter 1. Corresponding Angles
2. Give two examples of corresponding angles in the diagram:
3. Find the value of x:
4. Are the lines parallel? Why or why not?
5. Are the lines parallel? Justify your answer.
For 6-10, what does the value of x have to be to make the lines parallel?
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6.
7.
8.
9.
10.
If m6
If m6
If m6
If m6
If m6
1 = (6x − 5)◦ and m6
2 = (3x − 4)◦ and m6
3 = (7x − 5)◦ and m6
4 = (5x − 5)◦ and m6
2 = (2x + 4)◦ and m6
5 = (5x + 7)◦ .
6 = (4x − 10)◦ .
7 = (5x + 11)◦ .
8 = (3x + 15)◦ .
6 = (5x − 2)◦ .
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 3.3.
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