Lesson 10.1 Skills Practice
Name________________________________________________________ Date__________________________
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.
Parallel lines
2.
Intersecting lines
are lines in a plane that cross or intersect each other.
3.
Coincidental lines
are lines that have equivalent linear equations and overlap at every point
are lines that lie in the same plane and do not intersect.
when they are graphed.
4.
Perpendicular lines
5.
Skew lines
6.
Coplanar lines
are lines that intersect at a right angle.
are lines that do not lie in the same plane.
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,
parallel lines, coplanar lines
coplanar lines
Chapter 10 Skills Practice • 711
Lesson 10.1 Skills Practice
page 2
4.
3.
coincidental lines, coplanar lines
coplanar lines, intersecting lines
5.
6.
intersecting lines, coplanar lines
skew lines
Sketch an example of each relationship.
Answers will vary.
8. coplanar lines
© 2011 Carnegie Learning
7. parallel lines
712 • Chapter 10 Skills Practice
Lesson 10.1 Skills Practice
page 3
Name________________________________________________________ Date__________________________
9. intersecting lines
10. perpendicular lines
11. coincidental 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
Case 1
Chapter 10 Skills Practice • 713
Lesson 10.1 Skills Practice
15.
page 4
16.
Case 1
Case 3
17.
18.
Case 3
© 2011 Carnegie Learning
Case 4
714 • Chapter 10 Skills Practice
Lesson 10.1 Skills Practice
page 5
Name________________________________________________________ Date__________________________
Use the map to give an example of each relationship.
N
W
E
S
Magnolia Drive
South
Daisy
Lane
North
Daisy
Lane
Cherry Street
19. intersecting lines
Plum Street
Ivy Lane
Chestnut
Street
20. perpendicular lines
Answers will vary.
Answers will vary.
Ivy Lane and Plum Street
Magnolia Drive and Cherry Street
21. parallel lines
Answers will vary.
22. skew lines
None. All streets are in the same plane.
© 2011 Carnegie Learning
Cherry Street and Chestnut Street
23. coincidental lines
North Daisy Lane and South Daisy Lane
24. coplanar lines
Answers will vary.
All streets are in the same plane.
Chapter 10 Skills Practice • 715
© 2011 Carnegie Learning
716 • Chapter 10 Skills Practice
Lesson 10.2 Skills Practice
Name_________________________________________________________ Date__________________________
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
b. linear pair of angles
2. Two angles whose sum is 180 degrees
b. linear pair of angles
a. supplementary angles
Problem Set
Sketch an example of each relationship.
Answers will vary.
1. congruent figures
2. congruent angles
© 2011 Carnegie Learning
30°
3. adjacent angles
30°
4. vertical angles
60°
60°
Chapter 10 Skills Practice • 717
Lesson 10.2 Skills Practice
5. linear pair
page 2
6. supplementary angles
140°
35°
40°
145°
Use the map to give an example of each relationship.
Willow Drive
Answers will vary.
1
2
5
9
10
15
6
11
16
12
17
3
4
7
8
Main Street
13 14 Franklin Drive
18
19 20
21
Si
xth
7. congruent angles
3 and 4
9. supplementary angles
9 and 10
11. adjacent angles
17 and 18
718 • Chapter 10 Skills Practice
22
24
Av
e
8. vertical angles
2 and 5
10. linear pair
11 and 12
12. vertical angles
12 and 17
Fif
th
Av
e
© 2011 Carnegie Learning
23
Lesson 10.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Complete each sketch.
Answers may vary.
13. Draw 2 adjacent to /1.
1
2
14. Draw /2 such that it forms a vertical angle with /1.
1
2
15. Draw /2 such that it supplements /1 and does not share a common side.
155°
25°
© 2011 Carnegie Learning
16. Draw /2 adjacent to /1.
2
1
Chapter 10 Skills Practice • 719
Lesson 10.2 Skills Practice
page 4
17. Draw /1 such that it forms a vertical angle with /2.
1
2
18. Draw /2 such that it forms a linear pair with /1.
2
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°
720 • Chapter 10 Skills Practice
© 2011 Carnegie Learning
42 1 x 5 180
Lesson 10.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
20. If /1 and /2 are supplementary angles and m/1 5 101°, what is m/2?
m1 1 m2 5 180
101 1 x 5 180
x 5 79
m2 5 79°
21. If /1 and /2 form a linear pair and m/1 is one-fifth m/2, what is the measure of each angle?
m1 1 m2 5 180
0.2x 1 x 5 180
1.2x 5 180
x 5 150 and 0.2x 5 0.2(150) 5 30
m2 5 150° and m1 5 30°
© 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?
m1 1 m2 5 180
(x 2 60) 1 x 5 180
2x 5 240
x 5 120 and x 2 60 5 120 2 60 5 60
m2 5 120° and m1 5 60°
Chapter 10 Skills Practice • 721
Lesson 10.2 Skills Practice
page 6
23. If /1 and /2 form a linear pair and m/1 is three times m/2, what is the measure of each angle?
m1 1 m2 5 180
3x 1 x 5 180
4x 5 180
x 5 45 and 3x 5 3(45) 5 135
m2 5 45° and m1 5 135°
24. If /1 and /2 are supplementary angles and m/1 is 12° more than m/2, what is the measure of
each angle?
m1 1 m2 5 180
(x 1 12) 1 x 5 180
2x 5 168
x 5 84 and x 1 12 5 84 1 12 5 96
© 2011 Carnegie Learning
m2 5 84° and m1 5 96°
722 • Chapter 10 Skills Practice
Lesson 10.3 Skills Practice
Name_________________________________________________________ Date__________________________
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
alternate interior angles
same-side interior angles
1. alternate exterior angles
same-side exterior angles
Alternate exterior angles
are pairs of angles formed when a third line (transversal)
intersects two other lines. These angles are on opposite sides of the transversal and are outside
the other two lines.
2. A
3.
transversal
Same-side exterior angles
is a line that intersects two or more lines.
are pairs of angles formed when a third line (transversal)
intersects two other lines. These angles are on the same side of the transversal and are outside
the other two lines.
4.
Alternate interior angles
are pairs of angles formed when a third line (transversal)
intersects two other lines. These angles are on opposite sides of the transversal and are in
between the other two lines.
5.
Same-side interior angles
are pairs of angles formed when a third line (transversal)
© 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.
Chapter 10 Skills Practice • 723
Lesson 10.3 Skills Practice
page 2
Problem Set
Sketch an example of each.
Answers will vary.
2. Alternate interior angles
1
3. Alternate exterior angles
1
4. Same-side interior angles
1
2
5. Same-side exterior angles
724 • Chapter 10 Skills Practice
2
6. Corresponding angles
2
1
2
2
1
© 2011 Carnegie Learning
1. Transversal
Lesson 10.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
Use the map to give an example of each type of relationship.
Answers will vary.
Taylor Ave
1
3 4
5 6
2
7 8
9 10
15
M
19
21
Way
k
l
Po
22
7. transversal
Hoover Ave. is a transversal that
20
12
17
18
14
13
23 24
27 28
25 26
29 30
Hoover
Ave
Roosevelt Ave
11
16
Wilson
Ave
e Dr
onro
8. alternate interior angles
8 and 5
intersects Monroe Dr. and Polk Way.
9. alternate exterior angles
© 2011 Carnegie Learning
11 and 18
11. same-side exterior angles
18 and 13
10. same-side interior angles
12 and 15
12. corresponding angles
24 and 28
Chapter 10 Skills Practice • 725
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
supplementary
.
are
15. The alternate exterior angles formed when two parallel lines are intersected by a transversal
congruent
.
are
16. The same-side exterior angles formed when two parallel lines are intersected by a transversal
supplementary
.
are
Determine the measure of all the angles in each.
17.
152°
28°
28°
152°
28°
152°
152°
28°
18. 36°
144°
144°
36°
36°
144°
144°
4x°
x°
36°
x 1 4x 5 180
x 5 36
4x 5 144
726 • Chapter 10 Skills Practice
© 2011 Carnegie Learning
5x 5 180
Lesson 10.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
19.
20.
80°
100°
x° 20 x°
100° 80°
80° 100°
100° 80°
3
75° 105°
105° 75°
4
75° 105°
105° 75°
75° 105°
105° 75°
75° 105°
105° 75°
1
2
x 2 20 1 x 5 180
2x 2 20 5 180
2x 5 200
x 5 100
© 2011 Carnegie Learning
x 2 20 5 80
Chapter 10 Skills Practice • 727
Lesson 10.3 Skills Practice
page 6
22. Solve for the value of x given
21. Solve for the value of x and y
given that ℓ1  ℓ2.
that ℓ1  ℓ2.
1
2
x°
1
66°
66°
2
66°
55° 55°
66°
70°
125°
x° 55°
110°
y°
66 1 90 1 y 5 180
y 5 24
66 1 90 1 x 5 180
© 2011 Carnegie Learning
x 5 24
728 • Chapter 10 Skills Practice
Lesson 10.4 Skills Practice
Name_________________________________________________________ Date__________________________
Parallel or Perpendicular?
Slopes of Parallel and Perpendicular Lines
Vocabulary
Define each term in your own words.
1. Reciprocal
When the product of two numbers is 1, the numbers are reciprocals of one another.
2. Negative reciprocal
When the product of two numbers is 21, the numbers are negative reciprocals of
one another.
Problem Set
Determine the slope of a line parallel to the given line represented by each equation.
1. y 5 6x 1 12
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
The slope of the line is 25, so the
slope of a line parallel to it is 25.
2  ​ x 2 5
2. y 5 ​ __
3
__ 
The slope of the line is ​ 2 ​ , so the
3
slope of a line parallel to it is ​ 2 ​ .
3
1  ​ x
4. y 5 14 2 ​ __
4
__ 
__ 
The slope of the line is 2​ 1 ​ , so the
4
slope of a line parallel to it is 2​ 1 ​ .
4
__ 
Chapter 10 Skills Practice • 729
Lesson 10.4 Skills Practice
page 2
5. 3x 1 4y 5 24
6. 15x 2 5y 5 40
3x 1 4y 5 24
15x 2 5y 5 40
4y 5 24 2 3x
25y 5 40 2 15x
y 5 6 2 ​ 3  ​ x
4
y 5 28 1 3x
__ 
__ 
The slope of the line is 2​ 3 ​  , so the
4
slope of a line parallel to it is 2​ 3 ​  .
4
The slope of the line is 3, so the
__ 
slope of a line parallel to it is 3.
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 8
The equations (a) and (c) represent parallel lines.
8. a. y 5 6 2 3x
b. y 5 23x 2 8
slope 5 23
The equations (a) and (b) represent parallel lines.
9. a. 5y 5 220x 2 45
slope 5 23
c. y 5 3x 1 10
slope 5 3
b. 2y 5 4x 1 6
c. 4y 5 32 2 16x
4y 5 32 2 16x
5y 5 220x 2 45
2y 5 4x 1 6
y 5 24x 2 9
y 5 2x 1 3
slope 5 24
The equations (a) and (c) represent parallel lines.
730 • Chapter 10 Skills Practice
slope 5 2
y 5 8 2 4x
slope 5 24
© 2011 Carnegie Learning
slope 5 28
c. y 5 4 1 8x
Lesson 10.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
10. a. 4y 5 4x 2 16
4y 5 4x 2 16
y 5 x 2 4
b. 2y 5 8 1 4x
2y 5 8 1 4x
y 5 4 1 2x
slope 5 1
slope 5 2
The equations (b) and (c) represent parallel lines.
11. a. 3x 1 5y 5 60
3x 1 5y 5 60
5y 5 23x 1 60
y 5 2​ 3 ​  x 1 12
5
__ 
__ 
slope 5 2​ 3  ​
5
3y 5 6x 1 18
y 5 2x 1 6
slope 5 2
b. 6x 1 10y 5 240
c. 15x 1 9y 5 18
6x 1 10y 5 240
15x 1 9y 5 18
10y 5 26x 2 40
___ 
3 ​   x 2 4
y 5 2​ __
5
3  ​ 
slope 5 2​ __
y 5 2​  6  ​ x 2 4
10
5
9y 5 215x 1 18
___ 
5 ​   x 1 2
y 5 2​ __
3
5 ​  
slope 5 2​ __
y 5 2​ 15 ​  x 1 2
9
3
The equations (a) and (b) represent parallel lines.
© 2011 Carnegie Learning
c. 3y 5 6x 1 18
Chapter 10 Skills Practice • 731
Lesson 10.4 Skills Practice
12. a. 2x 1 8y 5 24
page 4
b. 232x 1 4y 5 12
c. 240x 1 5y 5 10
232x 1 4y 5 12
240x 1 5y 5 10
2x 1 8y 5 24
8y 5 x 1 24
4y 5 32x 1 12
y 5 ​ 1 ​  x 1 3
8
__ 
y 5 8x 1 3
__ 
slope 5 ​ 1 ​ 
8
The equations (b) and (c) represent parallel lines.
slope 5 8
5y 5 40x 1 10
y 5 8x 1 2
slope 5 8
Determine the negative reciprocal of each number.
1
2​ __ ​
5
1 ​
 ​__
7
3  ​
15. ​ __
4
4
2​   ​
3
5
16. 2​ __  ​ 8
1  ​ 17. ​ __
7
2
18. 2​ __  ​ 5
14. 27 8 ​
 ​__
5
732 • Chapter 10 Skills Practice
27
__ 
5 ​
 ​__
2
© 2011 Carnegie Learning
13. 5 Lesson 10.4 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
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
1  ​ x 1 4
21. y 5 ​ __
6
__ 
a line perpendicular to it is 2​ 1  ​.
5 1  ​ x
22. y 5 9 2 ​ __
3
__ 
The slope of the line is ​ 1 ​ , so the
6 slope of a line perpendicular to it is 26.
© 2011 Carnegie Learning
The slope of the line is 5, so the slope of
__ 
The slope of the line is 2​ 1 ​ , so the
3 slope of a line perpendicular to it is 3.
23. 5x 1 6y 5 36
24. 4x 2 3y 5 21
5x 1 6y 5 36
4x 2 3y 5 21
6y 5 25x 1 36
23y 5 24x 1 21
y 5 2​ 5  ​ x 1 6
6
__ 
y 5 ​ 4  ​ x 2 7
3
__ 
The slope of the line is 2​ 5 ​ , so the
6 slope of a line perpendicular to it is ​ 6 ​ .
5 __ 
__ 
__ 
The slope of the line is ​ 4 ​ , so the
3 slope of a line perpendicular to it is 2​ 3 ​ .
4 __ 
Chapter 10 Skills Practice • 733
Lesson 10.4 Skills Practice
page 6
Identify the slope of the line represented by each equation to determine which equations represent
perpendicular lines.
25. a. y 5 __
​ 2 ​  x 2 8 3
__ 
3  ​ x 2 1
b. y 5 ​ __
2
__ 
slope 5 ​ 3 ​ 
2
slope 5 ​ 2 ​ 
3
The equations (a) and (c) represent perpendicular lines.
26. a. y 5 25x 2 23
c. y 5 5x 1 31
slope 5 ​ 1 ​ 
5
slope 5 5
__ 
slope 5 25
The equations (a) and (b) represent perpendicular lines.
b. 2y 5 3x 1 8
c. 29y 5 6x 1 9
2y 5 3x 1 8
29y 5 6x 1 9
26y 5 24x 1 12
__ 
y 5 __
​ 3 ​   x 1 4
2
y 5 __
​ 2 ​   x 2 2
slope 5 __
​ 3 ​  
3
2
slope 5 __
​ 2 ​
  
The equations (b) and (c) represent perpendicular lines.
y 5 ​ 4 ​  x 2 2
6
3
__ 
2  ​  x 2 1
y 5 2​ __
3
2 ​  
slope 5 2​ __
y 5 2​ 6  ​ x 2 1
9
3
© 2011 Carnegie Learning
__ 
slope 5 2​ 3 ​ 
2
1  ​ x
b. y 5 18 1 ​ __
5
27. a. 26y 5 24x 1 12
3  ​ x 1 14
c. y 5 2 ​ __
2
734 • Chapter 10 Skills Practice
Lesson 10.4 Skills Practice
page 7
Name_________________________________________________________ Date__________________________
28. a. 25y 5 25x 1 55
b. 5y 5 x 1 15
c. 4y 5 20x 2 24
25y 5 25x 1 55
5y 5 x 1 15
4y 5 20x 2 24
y 5 25x 2 11
y 5 ​ 1 ​  x 1 3
5
__ 
__ 
slope 5 25
The equations (a) and (b) represent perpendicular lines.
29. a. 26x 1 2y 5 20
26x 1 2y 5 20
2y 5 6x 1 20
y 5 3x 1 10
slope 5 3
slope 5 5
b. 29x 2 3y 5 218
c. x 1 3y 5 15
29x 2 3y 5 218
x 1 3y 5 15
23y 5 9x 2 18
y 5 23x 1 6
slope 5 23
3y 5 2x 1 15
__ 
y 5 2​ 1 ​  x 1 5
3
__ 
slope 5 2​ 1 ​ 
3
The equations (a) and (c) represent perpendicular lines.
© 2011 Carnegie Learning
slope 5 ​ 1 ​ 
5
y 5 5x 2 6
Chapter 10 Skills Practice • 735
Lesson 10.4 Skills Practice
30. a. 3x 1 18y 5 272
page 8
b. 30x 1 5y 5 25
c. 22x 1 12y 5 224
30x 1 5y 5 25
22x 1 12y 5 224
3x 1 18y 5 272
18y 5 23x 2 72
5y 5 230x 1 25 12y 5 2x 2 24
___ 
slope 5 26 y 5 __
1 ​   x 2 4
​ 1 ​   x 2 2
y 5 2​ __
6
6
1 ​ slope 5 2​ __
  
slope 5 __
​ 1 ​  
6
3
y 5 2​ ___  ​ x 2 4
18
y 5 26x 1 5 y 5 ​  2  ​ x 2 2
12
6
The equations (b) and (c) represent perpendicular lines.
Determine whether the lines described by the equations are parallel, perpendicular, or neither.
31. y 5 5x 1 8
slope 5 5
y 5 4 1 5x
slope 5 5
The slopes are equal, so the lines are parallel.
slope 5 22
1  ​ x 1 17
y 5 ​ __
2
__ 
slope 5 ​ 1 ​ 
2
The product of the slopes is 21, so the lines are perpendicular.
33. y 5 __
​ 1 ​  x 1 5
3
__ 
slope 5 ​ 1 ​ 
3
y 5 3x 2 2
slope 5 3
The product of the slopes is not 21, and the slopes are not equal, so the lines are not parallel or
perpendicular.
736 • Chapter 10 Skills Practice
© 2011 Carnegie Learning
32. y 5 15 2 2x
Lesson 10.4 Skills Practice
page 9
Name_________________________________________________________ Date__________________________
34. 3x 1 12y 5 24
220x 1 5y 5 40
3x 1 12y 5 24
220x 1 5y 5 40
12y 5 23x 1 24
y 5 2​  3  ​ x 1 2
12
y 5 2​ 1 ​  x 1 2
4
___ 
__ 
5y 5 20x 1 40
y 5 4x 1 8
slope 5 4
__ 
slope 5 2​ 1  ​
4
© 2011 Carnegie Learning
The product of the slopes is 21, so the lines are perpendicular.
35. 3x 1 2y 5 2
2x 1 3y 5 3
3x 1 2y 5 2
2x 1 3y 5 3
2y 5 23x 1 2
y 5 2​ 3 ​  x 1 1
2
__ 
__ 
slope 5 2​ 3 ​ 
2
3y 5 22x 1 3
__ 
y 5 2​ 2  ​ x 1 1
3
__ 
slope 5 2​ 2 ​ 
3
The product of the slopes is not 21, and the slopes are not equal, so the lines are neither
parallel nor perpendicular.
Chapter 10 Skills Practice • 737
Lesson 10.4 Skills Practice
page 10
36. 10y 5 6x 1 80
212x 1 20y 5 160
10y 5 6x 1 80
212x 1 20y 5 160
___ 
y 5 __
​ 3 ​   x 1 8
5
slope 5 __
​ 3 ​  
y 5 ​  6  ​x 1 8
10
20y 5 12x 1 160
___ 
3  ​  x 1 8
y 5 ​ __
y 5 ​ 12 ​  x 1 8
20
5
__ 
5
slope 5 ​ 3  ​
5
© 2011 Carnegie Learning
The slopes are equal, so the lines are parallel.
738 • Chapter 10 Skills Practice
Lesson 10.5 Skills Practice
Name_________________________________________________________ Date__________________________
Up, Down, and All Around
Line Transformations
Vocabulary
Write a definition for the term in your own words.
1. Triangle Sum Theorem
The Triangle Sum Theorem states that the sum of the measures of the three interior angles of a
triangle is equal to 180°.
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
–8
–6
–4
–2
2
D
C
4
2
B
A
2
4
6
8
x
–2
© 2011 Carnegie Learning
_______ 
 ​ 
5 ______
​ 3 2 1 
622
5 __
​ 2 ​  
4
y 2y
 
line CD: m 5 _______
​ x 2 x  ​ 
 ​ 
5 ______
​ 7 2 5 
622
5 __
​ 2 ​  
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
–4
–6
–8
1
2
1
2
1
4
Line AB is parallel to line CD.
Chapter 10 Skills Practice • 739
Lesson 10.5 Skills Practice
page 2
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
2
6
A
4
2
–8
–6
–4
–2
2
D4
6
8
x
1
7
_______ 
0 2 (23)
5 ________
​ 
 
 ​ 
y 2y
line CD: m 5 ​ x2 2 x1 
 ​
–2
C
_______ 
5 ________
​  8 2 5 
 ​ 
3 2 (24)
5 __
​ 3 ​  
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
–4
2
–6
–8
1
3 2 (24)
__ 
5 ​ 3 ​ 
7
Line AB is parallel to line CD.
3. Horizontally translate line AB 25 units to create line CD. Calculate the slope of each line to
determine if the lines are parallel.
2
6
4
–8 –6
C
2
A
–4 –2
B
2
4
6
8
x
–4
_______ 
2 2 (21)
 
 ​ 
5 __________
​ 
23 2 (28)
5 __
​ 3 ​  
2
–6
–8
740 • Chapter 10 Skills Practice
5
y 2y
line CD: m 5 ​ x2 2 x1 
 ​
–2
Line AB is parallel to line CD.
1
5
1
© 2011 Carnegie Learning
8
D
_______ 
2 2 (21)
 ​ 
5 ________
​ 
 
2 2 (23)
5 __
​ 3 ​  
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
Lesson 10.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________
4. Horizontally translate line AB 6 units to create line CD. Calculate the slope of each line to
determine if the lines are parallel.
2
8
6
4
2
B
D
–8
–6
–4
–2
2
4
6
8
x
1
1 2 (22)
__ 
5 ​ 6 ​ 
3
_______ 
y 2y
line CD: m 5 ​ x2 2 x1 
 ​
–2
A
_______ 
1 2 (25)
 ​ 
5 ________
​ 
 
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
–4
2
C
–6
–8
1
________ 
5 __
​ 6 ​  
3
1 2 (25)
5 ​ 
 ​ 
724
Line AB is parallel to line CD.
5. Vertically translate line AB 7 units to create line CD. Calculate the slope of each line to determine if
the lines are parallel.
line CD:
y 2y
m 5 ​ x2 2 x1 ​ 
6
4
© 2011 Carnegie Learning
2
8
C
_______ 
 ​ 
5 ________
​  24 2 1 
2 2 (23)
5 ___
​ 25 ​ 
 
y 2y
 ​
line AB: m 5 ​ x2 2 x1 
y
D
2
A
–8
–6
–4
–2
2
4
6
8
x
–2
–4
1
5
_______ 
3 2 8 
 ​ 
5 ​ ________
2 2 (23)
5 ___
​ 25 ​ 
 
2
B
–6
–8
1
5
Line AB is parallel to line CD.
Chapter 10 Skills Practice • 741
Lesson 10.5 Skills Practice
page 4
6. Horizontally translate line AB 23 units to create line CD. Calculate the slope of each line to
determine if the lines are parallel.
2
8
6
4
2
–8
–6
–4
A
C
–2
2
4
6
8
x
D
1
2
_______ 
24 2 1 
5 ​ __________
 ​ 
22 2 (24)
5 ___
​ 25 ​ 
 
y 2y
line CD: m 5 ​ x2 2 x1 
 ​
–2
–4
_______ 
5 ________
​  24 2 1 
 ​ 
1 2 (21)
5 ___
​ 25 ​ 
 
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
B
2
–6
–8
1
2
Line AB is parallel to line CD.
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.
6
C
B
A
2
–8
–6
–4
–2
2
4
6
8
x
1
3
_______ 
y 2y
line AC: m 5 ​ x2 2 x1 
 ​
–2
–4
2
–6
–8
1
______ 
3 ​  
5 2 ​ __
 ​
5 ​ 6 2 3 
022
2
Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other.
742 • Chapter 10 Skills Practice
© 2011 Carnegie Learning
2
8
4
_______ 
 ​ 
5 ______
​ 5 2 3 
522
5 __
​ 2 ​  
y 2y
line AB: m 5 ​ x2 2 x1 
 ​
y
Lesson 10.5 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
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.
2
8
C
6
B
4
2
–8
–6
–4
_______ 
 ​ 
5 ______
​ 4 2 0 
321
5 __
​ 4 ​  
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
A2
–2
4
6
8
x
1
2
_______ 
4 2 6 
5 ​ ________
 ​ 
y 2y
line BC: m 5 ​ x 2 2 x 1 ​ 
–2
2
–4
–6
3 2 (21)
__ 
–8
1
5 2​ 2 ​ 
4
Line AB is perpendicular to line BC because the slopes are negative reciprocals of each other.
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.
2
© 2011 Carnegie Learning
8
6
C
4
–6
–4
–2
2
–2
4
6
8
x
B
–4
–6
–8
1
1 2 (24)
__ 
y 2y
line AC: m 5 _______
​ x 2 x  ​ 
 
 ​ 
5 ________
​  6 2 1 
0 2 (24)
5 __
​ 5 ​  
2
A
–8
_______ 
 ​ 
5 ________
​  23 2 1 
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
5 2​ 4 ​ 
5
2
1
2
1
4
Line AB is perpendicular to line AC because the slopes are negative reciprocals of
each other.
Chapter 10 Skills Practice • 743
Lesson 10.5 Skills Practice
page 6
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.
2
8
6
4
A
–8
–6
–4
2
4
C
6
8
1
21 2 (22)
__ 
_______ 
22 2 (21)
5 __________
​ 
 
 ​ 
21 2 4
5 __
​ 1 ​  
5 2​ 5 ​ 
1
y 2y
line BC: m 5 ​ x2 2 x1 
 ​
1
1
2
–2
_______ 
 ​ 
5 __________
​  22 2 3 
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
x
B
–4
–6
–8
5
Line AB is perpendicular to line BC because the slopes are negative reciprocals of each other.
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.
_______ 
5 __________
​  6 2 2  ​ 
21 2 (24)
4 ​  
5 ​ __
3
y 2y
 
line AC: m 5 _______
​ x 2 x  ​ 
5 ________
​  21 2 2 
 ​ 
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
2
8
B
6
4
2
A
–8
–6
–4
–2
–2C
2
4
6
8
x
–4
–6
1
2
1
2
1
0 2 (24)
–8
__ 
5 2​ 3 ​ 
4
Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other.
744 • Chapter 10 Skills Practice
© 2011 Carnegie Learning
y
Lesson 10.5 Skills Practice
page 7
Name_________________________________________________________ Date__________________________
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.
2
8
6
4
–6
–4
__ 
_______ 
23 2 (27)
 ​ 
5 __________
​ 
 
5 2 (21)
5 __
​ 4 ​  
5 2​ 6 ​ 
4
y2 2 y1
line BC: m 5 ​ x 2 x  
 ​
2
1
–2
2
4
6
8
x
–2
B
–4
1
521
A
2
–8
_______ 
5 _______
​ 23 2 3 ​ 
 
y 2y
line AB: m 5 ​ x2 2 x1 ​ 
y
–6
C
–8
6
Line AB is perpendicular to line BC because the slopes are negative reciprocals of each other.
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.
y
8
B
© 2011 Carnegie Learning
6
2
–8
–6
–4C –2
G–2
–4
D
H
–6
–8
__ 
___
__ 
slope of EF 
​  
​5 ​ 2 ​ 
5
F
4
A
___
slope of AB 
​  
​5 ​ 2 ​ 
5
___ ___
​   EF 
AB ​
​  
​
E
2
4
6
8
x
___
__ 
____
__ 
slope of CD ​
​  5 ​ 5 ​ 
2
slope of GH ​
​  5 ​ 5 ​ 
2
___ ____
​  
CD 
​ GH 
​  
​
Chapter 10 Skills Practice • 745
Lesson 10.5 Skills Practice
y
8
6
E
A
2
F
–6
C
–4
–2
2
B4
6
x
8
–2
–4 D
G
–6
H
–8
15.
y
8
6
2
–6
G
–4
–2
2
4
6
8
–4
H
16.
–6
–4
____
__ 
–8
D
CD 
​ GH 
​  
​
​  
___ ____
4
–2
4
–2
–4
___
__ 
___
__ 
____
__ 
___ ___
6
8
H
C
x
slope of CD ​
​  5 ​ 6 ​ 
2
slope of GH ​
​  5 ​ 6 ​ 
2
–6
–8
__ 
AB ​
​  
​
​   EF 
D
2
___
slope of AB 
​  
​5 ​ 2 ​ 
6
slope of EF 
​  
​5 ​ 2 ​ 
6
B
2
–8
__ 
slope of GH ​
​  5 2​ 6 ​ 
2
8
F
6
A
___
–6
y
E
__ 
slope of CD ​
​  5 2​ 6 ​ 
2
x
–2
C
___
AB ​
​  
​
​   EF 
B
–8
__ 
___ ___
F
A
___
​5 2​ 2 ​ 
slope of AB 
​  
6
slope of EF 
​  
​5 2​ 2 ​ 
6
E
4
__ 
___
6 ​  
​5 2​ __
slope of EF 
​  
2
___ ___
AB ​
​  
​
​   EF 
___
2 ​  
slope of CD ​
​  5 2​ __
6
____
2 ​  
slope of GH ​
​  5 2​ __
6
___ ____
CD 
​ GH 
​  
​
​  
4
–8
___
slope of AB ​
​  5 2​ 6 ​ 
2
G
746 • Chapter 10 Skills Practice
___ ____
CD 
​ GH 
​  
​
​  
© 2011 Carnegie Learning
14.
page 8
Lesson 10.5 Skills Practice
page 9
Name_________________________________________________________ Date__________________________
17.
y
8
E
6
A
4
F
–4
–2
–2
2
D
4
6
8
C
6
–2
–4
D
–6
___
__ 
___
__ 
____
__ 
AB ​
​  
​
​   EF 
C
4
6
G
8
x
slope of CD ​
​  5 ​ 6 ​ 
5
s lope of GH 
​  
​5 ​ 6 ​ 
5
___ ____
CD 
​ GH 
​  
​
​  
© 2011 Carnegie Learning
–8
H
__ 
___ ___
A
2
___
slope of AB ​
​  5 ​ 5 ​ 
6
slope of EF ​
​  5 ​ 5 ​ 
6
2
–2
__ 
___ ____
8
–4
B
____
CD 
​ GH 
​  
​
​  
y
–8 F –6
__ 
slope of GH ​
​  5 2​ 5 ​ 
3
–8
4
___
slope of CD ​
​  5 2​ 5 ​ 
3
x
G
–6
E
__ 
___ ___
–4
18.
___
AB ​
​  
​
​   EF 
H
–6
__ 
slope of EF ​
​  5 2​ 3 ​ 
5
B
2
–8
___
​5 2​ 3 ​ 
slope of AB 
​  
5
Chapter 10 Skills Practice • 747
© 2011 Carnegie Learning
748 • Chapter 10 Skills Practice