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Lesson 10.1
Skills Practice
1DPH _______________________________________________________ 'DWH _________________________
Location, Location, Location!
Line Relationships
Vocabulary
Write the term or terms from the box that best complete each statement.
intersecting lines
perpendicular lines
parallel lines
coplanar lines
skew lines
coincidental lines
1.
are lines that lie in the same plane and do not intersect.
2.
are lines in a plane that cross or intersect each other.
are lines that have equivalent linear equations and overlap at every point
3.
when they are graphed.
4.
are lines that intersect at a right angle.
5.
are lines that do not lie in the same plane.
6.
are lines that lie in the same plane.
Problem Set
Describe each sketch using the terms intersecting lines, perpendicular lines, parallel lines, coplanar
lines, skew lines, and coincidental lines. More than one term may apply.
2.
© 2011 Carnegie Learning
1.
perpendicular lines, intersecting lines,
coplanar lines
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Lesson 10.1
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3.
4.
5.
6.
Sketch an example of each relationship.
7. parallel lines
© 2011 Carnegie Learning
8. coplanar lines
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Lesson 10.1
Skills Practice
page 3
1DPH _______________________________________________________ 'DWH _________________________
9. intersecting lines
11. coincidental lines
10. perpendicular lines
12. skew lines
Choose the description from the box that best describes each sketch.
Case 1: Two or more coplanar lines intersect at a single point.
Case 2: Two or more coplanar lines intersect at an infinite number of points.
Case 3: Two or more coplanar lines do not intersect.
© 2011 Carnegie Learning
Case 4: Two or more are not coplanar.
13.
14.
Case 2
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16.
17.
18.
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Lesson 10.1
Skills Practice
page 5
1DPH _______________________________________________________ 'DWH _________________________
Use the map to give an example of each relationship.
N
19. intersecting lines
W
E
S
Magnolia Drive
South
Daisy
Lane
North
Daisy
Lane
Cherry Street
Plum Street
Ivy Lane
Chestnut
Street
20. perpendicular lines
Answers will vary.
© 2011 Carnegie Learning
Ivy Lane and Plum Street
21. parallel lines
22. skew lines
23. coincidental lines
24. coplanar lines
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Chapter 10
Skills Practice
Lesson 10.2
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
When Lines Come Together
Angle Relationships Formed by Two Intersecting Lines
Vocabulary
Match each definition to its corresponding term.
1. Two adjacent angles that form a straight line
a. supplementary angles
2. Two angles whose sum is 180 degrees
b. linear pair of angles
Problem Set
© 2011 Carnegie Learning
Sketch an example of each relationship.
1. congruent figures
2. congruent angles
3. adjacent angles
4. vertical angles
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Lesson 10.2
Skills Practice
5. linear pair
page 2
6. supplementary angles
Willow Drive
Use the map to give an example of each relationship.
1
2
5
9
10
15
6
11
16
4
7
8
Main Street
13 14 Franklin Drive
12
17
3
18
19 20
21
24
Si
xth
7. congruent angles
Av
e
8. vertical angles
/3 and /4
9. supplementary angles
11. adjacent angles
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10. linear pair
12. vertical angles
Skills Practice
Fif
th
Av
e
© 2011 Carnegie Learning
22
23
Lesson 10.2
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
Complete each sketch.
13. Draw /2 adjacent to /1.
1
2
14. Draw /2 such that it forms a vertical angle with /1.
1
15. Draw /2 such that it supplements /1 and does not share a common side.
155°
© 2011 Carnegie Learning
16. Draw /2 adjacent to /1.
1
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17. Draw /1 such that it forms a vertical angle with /2.
2
18. Draw /2 such that it forms a linear pair with /1.
1
Determine each unknown angle measure.
19. If /1 and /2 form a linear pair and m/1 5 42°, what is m/2?
m/1 1 m/2 5 180
x 5 138
m/2 5 138°
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© 2011 Carnegie Learning
42 1 x 5 180
Lesson 10.2
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
20. If /1 and /2 are supplementary angles and m/1 5 101°, what is m/2?
21. If /1 and /2 form a linear pair and m/1 is one-fifth m/2, what is the measure of each angle?
© 2011 Carnegie Learning
22. If /1 and /2 are supplementary angles and m/1 is 60° less than m/2, what is the measure of
each angle?
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23. If /1 and /2 form a linear pair and m/1 is three times m/2, what is the measure of each angle?
24. If /1 and /2 are supplementary angles and m/1 is 12° more than m/2, what is the measure of
© 2011 Carnegie Learning
each angle?
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Chapter 10
Skills Practice
Lesson 10.3
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Crisscross Applesauce
Angle Relationships Formed by Two Lines Intersected
by a Transversal
Vocabulary
Write the term from the box that best completes each sentence.
transversal
same-side interior angles
alternate interior angles
alternate exterior angles
same-side exterior angles
are pairs of angles formed when a third line (transversal)
1.
intersects two other lines. These angles are on opposite sides of the transversal and are outside
the other two lines.
2. A
is a line that intersects two or more lines.
are pairs of angles formed when a third line (transversal)
3.
intersects two other lines. These angles are on the same side of the transversal and are outside
the other two lines.
are pairs of angles formed when a third line (transversal)
4.
intersects two other lines. These angles are on opposite sides of the transversal and are in
between the other two lines.
are pairs of angles formed when a third line (transversal)
5.
© 2011 Carnegie Learning
intersects two other lines. These angles are on the same side of the transversal and are in
between the other two lines.
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Lesson 10.3
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Problem Set
1. Transversal
2. Alternate interior angles
3. Alternate exterior angles
4. Same-side interior angles
5. Same-side exterior angles
6. Corresponding angles
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Sketch an example of each.
Lesson 10.3
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
Use the map to give an example of each type of relationship.
Taylor Ave
1
3 4
5 6
2
7 8
9 10
15
e Dr
onro
11
Polk
Way
19
21
22
7. transversal
20
17
18
14
13
23 24
27 28
25 26
29 30
Hoover
Ave
Roosevelt Ave
12
Wilson
Ave
M
16
8. alternate interior angles
Hoover Ave. is a transversal that
intersects Monroe Dr. and Polk Way.
© 2011 Carnegie Learning
9. alternate exterior angles
11. same-side exterior angles
10. same-side interior angles
12. corresponding angles
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Lesson 10.3
Skills Practice
page 4
Complete each statement with congruent or supplementary.
13. The alternate interior angles formed when two parallel lines are intersected by a transversal
congruent
.
are
14. The same-side interior angles formed when two parallel lines are intersected by a transversal
.
are
15. The alternate exterior angles formed when two parallel lines are intersected by a transversal
.
are
16. The same-side exterior angles formed when two parallel lines are intersected by a transversal
.
are
Determine the measure of all the angles in each.
17.
152°
28°
28°
152°
28°
18.
28°
152°
152°
4x°
© 2011 Carnegie Learning
x°
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Lesson 10.3
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
19.
20.
x° 2 20 x°
,3
,4
75°
,1
© 2011 Carnegie Learning
,2
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Lesson 10.3
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page 6
22. Solve for the value of x given
21. Solve for the value of x and y
that ℓ1 i ℓ2.
given that ℓ1 i ℓ2.
,1
,2
x°
,1
66°
x°
55°
125°
,2
© 2011 Carnegie Learning
y°
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Chapter 10
Skills Practice
Lesson 10.4
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Parallel or Perpendicular?
Slopes of Parallel and Perpendicular Lines
Vocabulary
Define each term in your own words.
1. Reciprocal
2. Negative reciprocal
Problem Set
Determine the slope of a line parallel to the given line represented by each equation.
1. y 5 6x 1 12
2x 2 5
2. y 5 __
3
The slope of the line is 6, so the
© 2011 Carnegie Learning
slope of a line parallel to it is 6.
3. y 5 8 2 5x
1x
4. y 5 14 2 __
4
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Lesson 10.4
Skills Practice
5. 3x 1 4y 5 24
page 2
6. 15x 2 5y 5 40
Identify the slope of the line represented by each equation to determine which equations represent
parallel lines.
7. a. y 5 8x 2 5
b. y 5 7 2 8x
slope 5 8
slope 5 28
c. y 5 4 1 8x
slope 5 8
8. a. y 5 6 2 3x
b. y 5 23x 2 8
c. y 5 3x 1 10
9. a. 5y 5 220x 2 45
b. 2y 5 4x 1 6
c. 4y 5 32 2 16x
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Chapter 10
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The equations (a) and (c) represent parallel lines.
Lesson 10.4
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
b. 2y 5 8 1 4x
c. 3y 5 6x 1 18
11. a. 3x 1 5y 5 60
b. 6x 1 10y 5 240
c. 15x 1 9y 5 18
© 2011 Carnegie Learning
10. a. 4y 5 4x 2 16
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Lesson 10.4
12. a. 2x 1 8y 5 24
Skills Practice
b. 232x 1 4y 5 12
page 4
c. 240x 1 5y 5 10
13. 5
14. 27
3
15. __
4
1
17. __
7
2
18. 2__
5
1
2__
5
5
16. 2__
8
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Chapter 10
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Determine the negative reciprocal of each number.
Lesson 10.4
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
Determine the slope of a line perpendicular to the given line represented by each equation.
19. y 5 13x 1 22
20. y 5 5x 2 17
The slope of the line is 13, so the slope
1
of a line perpendicular to it is 2___ .
13
1x
22. y 5 9 2 __
3
23. 5x 1 6y 5 36
24. 4x 2 3y 5 21
© 2011 Carnegie Learning
1x 1 4
21. y 5 __
6
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Identify the slope of the line represented by each equation to determine which equations represent
perpendicular lines.
3x 2 1
b. y 5 __
2
2x 2 8
25. a. y 5 __
3
__
__
slope 5 3
2
slope 5 2
3
3 x 1 14
c. y 5 2__
2
__
slope 5 2 3
2
The equations (a) and (c) represent perpendicular lines.
1x
b. y 5 18 1 __
5
c. y 5 5x 1 31
27. a. 26y 5 24x 1 12
b. 2y 5 3x 1 8
c. 29y 5 6x 1 9
© 2011 Carnegie Learning
26. a. y 5 25x 2 23
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1DPH________________________________________________________ 'DWH _________________________
b. 5y 5 x 1 15
c. 4y 5 20x 2 24
29. a. 26x 1 2y 5 20
b. 29x 2 3y 5 218
c. x 1 3y 5 15
© 2011 Carnegie Learning
28. a. 25y 5 25x 1 55
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Lesson 10.4
Skills Practice
30. a. 3x 1 18y 5 272
b. 30x 1 5y 5 25
page 8
c. 22x 1 12y 5 224
Determine whether the lines described by the equations are parallel, perpendicular, or neither.
31. y 5 5x 1 8
y 5 4 1 5x
slope 5 5
slope 5 5
32. y 5 15 2 2x
1 x 1 17
y 5 __
2
1x 1 5
33. y 5 __
3
y 5 3x 2 2
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The slopes are equal, so the lines are parallel.
Lesson 10.4
Skills Practice
page 9
1DPH________________________________________________________ 'DWH _________________________
220x 1 5y 5 40
35. 3x 1 2y 5 2
2x 1 3y 5 3
© 2011 Carnegie Learning
34. 3x 1 12y 5 24
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Lesson 10.4
Skills Practice
212x 1 20y 5 160
© 2011 Carnegie Learning
36. 10y 5 6x 1 80
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Chapter 10
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Lesson 10.5
Skills Practice
1DPH________________________________________________________ 'DWH _________________________
Up, Down, and All Around
Line Transformations
Vocabulary
Write a definition for the term in your own words.
1. Triangle Sum Theorem
Problem Set
Sketch the translation for each line.
1. Vertically translate line AB 4 units to create line CD. Calculate the slope of each line to determine if
the lines are parallel.
8
6
D
C
4
2
–8
–6
–4
–2
B
A
2
4
6
–2
© 2011 Carnegie Learning
_______
321
5 ______
622
2
5 __
4
y 2y
line CD: m 5 _______
x 2x
725
5 ______
622
2
5 __
y 2y
line AB: m 5 x2 2 x1
2
1
y
–4
–6
–8
8
x
2
1
2
1
4
Line AB is parallel to line CD.
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Lesson 10.5
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2. Vertically translate line AB 28 units to create line CD. Calculate the slope of each line to determine
if the lines are parallel.
y
B
8
6
A
4
2
–8
–6
–4
–2
2
4
6
8
x
–2
–4
–6
–8
3. Horizontally translate line AB 25 units to create line CD. Calculate the slope of each line to
determine if the lines are parallel.
y
8
6
4
2
–8
–6
A
–4 –2
B
2
4
6
8
–4
–6
–8
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Skills Practice
Lesson 10.5
Skills Practice
page 3
1DPH________________________________________________________ 'DWH _________________________
4. Horizontally translate line AB 6 units to create line CD. Calculate the slope of each line to
determine if the lines are parallel.
y
8
6
4
2
–8
–6
–4
B
–2
2
4
6
8
x
–2
A
–4
–6
–8
5. Vertically translate line AB 7 units to create line CD. Calculate the slope of each line to determine if
the lines are parallel.
y
8
6
© 2011 Carnegie Learning
4
2
A
–8
–6
–4
–2
2
4
6
8
x
–2
–4
B
–6
–8
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Lesson 10.5
Skills Practice
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6. Horizontally translate line AB 23 units to create line CD. Calculate the slope of each line to
determine if the lines are parallel.
y
8
6
4
2
A
–8
–6
–4
–2
2
4
6
8
x
–2
–4
B
–6
–8
Sketch the rotation for each line.
7. Use point A as the point of rotation and rotate line AB 908 counterclockwise to form line AC.
Calculate the slope of each line to determine if the lines are perpendicular. Explain how you
determined your answer.
_______
523
5 ______
522
2
5 __
8
6
C
B
4
A
2
3
–8
–6
–4
–2
2
4
6
8
x
_______
623
5 ______
022
3
5 2 __
y 2y
line AC: m 5 x2 2 x1
2
1
–2
–4
–6
–8
2
Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other.
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© 2011 Carnegie Learning
y 2y
line AB: m 5 x2 2 x1
2
1
y
Lesson 10.5
Skills Practice
page 5
1DPH________________________________________________________ 'DWH _________________________
8. Use point B as the point of rotation and rotate line AB 908 clockwise to form line BC. Calculate the
slope of each line to determine if the lines are perpendicular. Explain how you determined your
answer.
y
8
6
B
4
2
–8
–6
–4
A2
–2
4
6
8
x
–2
–4
–6
–8
9. Use point A as the point of rotation and rotate line AB 908 counterclockwise to form line AC.
Calculate the slope of each line to determine if the lines are perpendicular. Explain how you
determined your answer.
y
© 2011 Carnegie Learning
8
6
4
2
A
–8
–6
–4
–2
2
–2
4
6
8
x
B
–4
–6
–8
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10. Use point B as the point of rotation and rotate line AB 908 clockwise to form line BC. Calculate the
slope of each line to determine if the lines are perpendicular. Explain how you determined your
answer.
y
8
6
4
A
–8
–6
–4
2
–2
2
4
6
8
x
B
–4
–6
–8
11. Use point A as the point of rotation and rotate line AB 908 clockwise to form line AC. Calculate the
slope of each line to determine if the lines are perpendicular. Explain how you determined your
answer.
y
8
B
6
2
A
–8
–6
–4
–2
2
4
6
8
–2
–4
–6
–8
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Lesson 10.5
Skills Practice
page 7
1DPH________________________________________________________ 'DWH _________________________
12. Use point B as the point of rotation and rotate line AB 908 counterclockwise to form line BC.
Calculate the slope of each line to determine if the lines are perpendicular. Explain how you
determined your answer.
y
8
6
4
A
2
–8
–6
–4
–2
2
4
6
8
x
–2
B
–4
–6
–8
Reflect line segment AB over the reflection line to form line segment CD. Reflect line segment EF over
the reflection line to form line segment GH. Calculate the slopes of all line segments to prove that the
line segments are parallel.
13.
8
B
© 2011 Carnegie Learning
6
–8
–6
–4C –2
G–2
–4
D
H
–6
–8
__
___
__
___
__
____
__
slope of EF 5 2
5
F
4
A
2
___
slope of AB 5 2
5
y
___ ___
AB i EF
E
2
4
6
8
x
slope of CD 5 5
2
slope of GH 5 5
2
___ ____
CD i GH
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Lesson 10.5
14.
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page 8
y
8
6
E
A
4
2
F
–8
–6
–4
–2
2
B4
6
x
8
–2
–4
–6
–8
y
15.
8
6
E
4
2
F
A
B
–8
–6
–4
–2
2
4
6
8
x
6
8
x
–2
–4
–6
–8
8
F
6
E
B
4
A
2
–8
–6
–4
–2
2
4
–2
–4
–6
–8
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y
16.
Lesson 10.5
Skills Practice
page 9
1DPH________________________________________________________ 'DWH _________________________
17.
y
8
E
6
A
4
F
B
2
–8
–6
–4
–2
2
4
6
8
x
4
6
8
x
–2
–4
–6
–8
18.
y
8
6
E
4
A
2
–8 F –6
–4
B
–2
2
–2
–4
–6
© 2011 Carnegie Learning
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