3­1 Parallel Lines 2011 October 04, 2011
3­1 Parallel Lines
Objective:
Discover angle relationships with parallel lines.
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3­1 Parallel Lines 2011 October 04, 2011
Warm­up:
Justify each statement.
a. If JK ≅ LM, then LM ≅ JK.
b. XY = XY c. If 2(3x ­ 7) = x + 5, then 6x ­ 14 = x + 5. d. If m<ABC + 40 = 85, then m<ABC = 45. e. If k = m and k + w = 12, then m + w = 12.
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3­1 Parallel Lines 2011 October 04, 2011
Working in pairs, each person will need:
Blank Paper
Protractor
Straightedge (Ruler)
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3­1 Parallel Lines 2011 October 04, 2011
Draw two parallel lines on your paper with a straightedge.
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3­1 Parallel Lines 2011 October 04, 2011
Draw two parallel lines on your paper with a straightedge.
Now draw a transversal that cuts both lines.
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3­1 Parallel Lines 2011 October 04, 2011
Measure all the angles and look for patterns.
Is your partner finding the same patterns?
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3­1 Parallel Lines 2011 October 04, 2011
!
t
n
e
m
h
c
a
t
t
A
the
n
e
Op
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3­1 Parallel Lines 2011 October 04, 2011
1
2
3
4
6
5
7
8
In this lesson we will talk about special angle pairs. Write down the following names and leave room to write about each type.
Alternate Interior Angles
Same-Side Interior Angles
Corresponding Angles
Alternate Exterior Angles
Same-Side Exterior Angles
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3­1 Parallel Lines 2011 October 04, 2011
1
2
3
4
6
5
7
8
Alternate Interior Angles
Same-Side Interior Angles
Corresponding Angles
Alternate Exterior Angles
Same-Side Exterior Angles
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3­1 Parallel Lines 2011 October 04, 2011
1
2
3
4
6
5
7
8
Alternate Interior Angles
Same-Side Interior Angles
Corresponding Angles
Alternate Exterior Angles
Same-Side Exterior Angles
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3­1 Parallel Lines 2011 October 04, 2011
1
2
3
4
6
5
7
8
Alternate Interior Angles
Same-Side Interior Angles
Corresponding Angles
Alternate Exterior Angles
Same-Side Exterior Angles
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3­1 Parallel Lines 2011 October 04, 2011
1
2
3
4
6
5
7
8
Alternate Interior Angles
Same-Side Interior Angles
Corresponding Angles
Alternate Exterior Angles
Same-Side Exterior Angles
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3­1 Parallel Lines 2011 October 04, 2011
1
2
3
4
6
5
7
8
Alternate Interior Angles
Same-Side Interior Angles
Corresponding Angles
Alternate Exterior Angles
Same-Side Exterior Angles
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3­1 Parallel Lines 2011 October 04, 2011
1
2
3
4
6
5
7
8
Alternate Interior Angles are _______________________
Same Side Interior Angles are _______________________
Corresponding Angles are ___________________________
Alternate Exterior Angles are _______________________
Same-Side Exterior Angles are ______________________
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3­1 Parallel Lines 2011 October 04, 2011
Examples: 1. Find the value of the missing angles and justify your reasoning.
b.
a.
v
22
y
x
w
103
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3­1 Parallel Lines 2011 October 04, 2011
Examples: 1. Find the value of the missing angles and justify your reasoning.
c.
w
y
78
39
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3­1 Parallel Lines 2011 October 04, 2011
2. Find the value of x and the measure of each labeled angle.
b.
a.
(2x + 10)
6x
70
4x
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3­1 Parallel Lines 2011 October 04, 2011
Check for Understanding
1. Find the measure of each angle in the diagram and justify your reasoning.
1 = 4 = 6 = 8 =
2 =
5 =
7 = 2. Use the numbered angles in the diagram to name a pair of
a. Alternate Interior Angles
b. Alternate Exterior Angles
c. Corresponding Angles
d. Same­Side Interior Angles
e. Same­Side Exterior Angles
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3­1 Parallel Lines 2011 October 04, 2011
HOMEWORK
Practice 3­1
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Attachments
Parallel Lines and Angle Relationships.gsp