lesson 3.1: parallel lines and transversals3.1 notes.notebook 3 november 10, 2018 activity 1 work...
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3.1 Notes.notebook
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November 10, 2018
Nov 103:40 PM
Lesson 3.1:Parallel Lines and
Transversals
3.1 Notes.notebook
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Essential Question
How can you describe angles formed by
parallel lines and transversals?
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Activity 1
Work with a partner.● Discuss what it means for two lines to be parallel.Decide on a strategy for drawing twoparallel lines. Then draw thetwo parallel lines.● Draw a third line that intersects the two parallel lines. This line is calleda transversal.
a. How many angles are formed by the parallel lines and the transversal? Label the angles.
b. Which of these angles have equal measures? Explain your reasoning.
The pairs of vertical angles are congruent, and so are the corresponding ones on the other parallel line. The transversal creates the same angles.
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Warm up
Use the figure.1. Identify the parallel lines.
2. Identify the transversal.
3. How many angles are formedby the transversal?
4. Which of the angles are congruent?
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Key Idea
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Example 1
Use the figure to find the measures of (a) ∠1 and (b) ∠2.
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On your own 12
Use the figure to find the measure of the angle. Explain your reasoning.
1. ∠1 2. ∠2
Corresponding
Supplementary
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Example 2
Use the figure to find the measures of the numbered angles.
<1 is vertical to the 75° angle.<1 = 75°
<6 is corresponding to the 75° angle.<6 = 75°
<4 is vertical to <6 and corresponding to <1.<4 = 75°
<2 is supplementary to the 75° angle.<2 = 105°
<3, <5, <7 = 105°
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On your own 3
3. Use the figure to find the measures of the numbered angles.
<2, <5, and <7 are all congruent tothe 59° angle.
<1, <3, <4, and <6 are all supplementaryto a 59° angle, and are therefore 121°.
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Example 3
A store owner uses pieces of tape to paint a window advertisement. The letters are slanted at an 80° angle. What is the measure of ∠1?
<1 is supplementary to the angle thatcorresponds to the 80° angle.
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Key Idea
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Example 4
The photo shows a portion of anairport. Describe the relationshipbetween each pair of angles.
a. ∠3 and ∠6
b. ∠2 and ∠7
Alternate exterior angles
Alternate interior angles
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On Your Own 57
In Example 4, the measure of ∠4 is 84°. Find the measure of the angle. Explain your reasoning.
5. ∠3 6. ∠5 7. ∠6
Supplementaryto <4
Alt. int. to <4Supplementaryto <5