Post on 19-Jan-2016
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Chapter 3 Review3.1: Vocabulary and Notation
3.2: Angles Formed by Parallel Lines and Transversals
3.3: Proving Lines are Parallel
3.4: Theorems about Perpendicular Lines
Name a pair of vertical angles.
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2 and 3
1 and 4
6 and 8
5 and 7
Name a pair of alternate interior angles.
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3 and 7
4 and 8
Name a pair of alternate exterior angles.
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2 and 5
1 and 6
Name a linear pair of angles.
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1 and 2
2 and 4
3 and 4
1 and 3
7 and 8
7 and 6
5 and 6
5 and 8
Name a pair of parallel lines.How do you know they are parallel?Name the transversal.
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m
n
r
m || n
arrows
r
Name a pair of corresponding angles.
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2 and 7
1 and 8
3 and 5
4 and 6
Describe the relationship between the lines using both words and math
notation.
x
y
Perpendicular; x y
Describe the relationship between the lines using both words and math
notation.
x
y
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Parallel; x || y
Name a pair of perpendicular segments.
P
Q
R
S
T
U
V
W
UW WV
Name a pair of skew segments.
P
Q
R
S
T
U
V
W
and
and
PQ TU
PW RS
Examples:
Name a pair of parallel segments.
P
Q
R
S
T
U
V
W
and TU WV
Name a pair of parallel planes.
P
Q
R
S
T
U
V
W
and plane QRT plane PSV
Write an equation that describes the relationship between the given angles. State the theorem or
postulate that justifies your equation.
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m
n
r
3 4 2m x 8 2 14m x
4 2 2 14 180x x Same-side interior angle theorem
Write an equation that describes the relationship between the given angles. State the theorem or
postulate that justifies your equation.
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m
n
r
2 3 7m x 7 34m x
3 7 34x x Corresponding Angles Postulate
Write an equation that describes the relationship between the given angles. State the theorem or
postulate that justifies your equation.
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m
n
r
7 2 2m x 8 5 45m x
2 2 5 45 180x x Linear Pair Theorem
Write an equation that describes the relationship between the given angles. State the theorem or
postulate that justifies your equation.
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m
n
r
3 4 2m x 7 5 37m x
4 2 5 37x x Alternate Interior Angles Theorem
Write an equation that describes the relationship between the given angles. State the theorem or
postulate that justifies your equation.
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m
n
r
2 8 12m x 5 2 4m x
8 12 2 4x x Alternate Exterior Angles Theorem
If 4 6, why is ?
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m
n
r
||m n
Converse of the Corresponding Angles Theorem
If 3 7, why is ?
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m
n
r
||m n
Converse of the alternate interior angles theorem
If 2 5, why is ?
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m
n
r
||m n
Converse of the alternate exterior angles theorem
If 4 and 7 are supplementary, why is ?
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m
n
r
||m n
Converse of the same-side interior angles theorem
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m
n
r
Find the value of x that would guarantee m || n.
4 3 9
7 2 4
m x
m x
4 7 180
3 9 2 4 180
5 5 180
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m m
x x
x
x
x
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m
n
r
Find the value of x that would guarantee m || n.
5 19
3 4 2
m x
m x
5 3
19 4 2
19 3 2
21 3
7
m m
x x
x
x
x
What do you know about x? Why?
10x
x>10: The shortest distance between a point not on a line and the line is the segment perpendicular to the segment.
What do you know about x? Why?
142 5x
2 5 14
2 9
4.5
x
x
x
Is this a perpendicular bisector? Why or why not?
No. We don’t know that the segment has been bisected or the angles formed are
right angles– no markings!
Is this a perpendicular bisector? Why or why not?
No. You can’t bisect a line– only a segment.
Is this a perpendicular bisector? Why or why not?
Yes. The SEGMENT has been cut in half and the figures intersect at 90°.
Given: h || p
Prove: 2 3
Statements Reasons
1. h || p 1. Given
2. 2. Corresponding angles theorem
3. 1 2 3.
4. 2 3 4.
h
p
12
3
1 3
Vertical angles theorem
Transitive Property of