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

5 185

37

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