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Location, Location, Location!Line Relationships
VocabularyWrite 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.
3. are lines that have equivalent linear equations and overlap at every point
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 SetDescribe each sketch using the terms intersecting lines, perpendicular lines, parallel lines, coplanar
lines, skew lines, and coincidental lines. More than one term may apply.
1.
perpendicular lines, intersecting lines,
coplanar lines
2.
Lesson 10.1 Skills Practice
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3. 4.
5. 6.
Sketch an example of each relationship.
7. parallel lines 8. coplanar lines
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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.
Case 4: Two or more are not coplanar.
13.
Case 2
14.
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Lesson 10.1 Skills Practice page 4
15. 16.
17. 18.
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Lesson 10.1 Skills Practice page 5
Name _______________________________________________________Date _________________________
Use the map to give an example of each relationship.
Mag
nolia
Driv
eCherry Street
Plum Street
Ivy Lane
ChestnutStreet
Nor
thD
aisy
Lane
Sou
thD
aisy
Lane
N
S
EW
19. intersecting lines
Answers will vary.
Ivy Lane and Plum Street
20. perpendicular lines
21. parallel lines 22. skew lines
23. coincidental lines 24. coplanar lines
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When Lines Come TogetherAngle Relationships Formed by Two Intersecting Lines
VocabularyMatch 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 SetSketch an example of each relationship.
1. congruent figures 2. congruent angles
3. adjacent angles 4. vertical angles
Lesson 10.2 Skills Practice
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Lesson 10.2 Skills Practice page 2
5. linear pair 6. supplementary angles
Use the map to give an example of each relationship.
13
21
23
119 1210 14
22
24
19 2015 16 17 18
31 2 4
75 86
Main Street
Franklin Drive
Fifth AveSixth Ave
Will
ow D
rive
7. congruent angles
3 and 4
8. vertical angles
9. supplementary angles 10. linear pair
11. adjacent angles 12. vertical angles
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Lesson 10.2 Skills Practice page 3
Name ________________________________________________________ Date _________________________
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°
16. Draw 2 adjacent to 1.
1
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Lesson 10.2 Skills Practice page 4
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 m1 5 42°, what is m2?
m1 1 m2 5 180
42 1 x 5 180
x 5 138
m2 5 138°
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Lesson 10.2 Skills Practice page 5
Name ________________________________________________________ Date _________________________
20. If 1 and 2 are supplementary angles and m1 5 101°, what is m2?
21. If 1 and 2 form a linear pair and m1 is one-fifth m2, what is the measure of each angle?
22. If 1 and 2 are supplementary angles and m1 is 60° less than m2, what is the measure of
each angle?
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Lesson 10.2 Skills Practice page 6
23. If 1 and 2 form a linear pair and m1 is three times m2, what is the measure of each angle?
24. If 1 and 2 are supplementary angles and m1 is 12° more than m2, what is the measure of
each angle?
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Crisscross ApplesauceAngle Relationships Formed by Two Lines Intersected by a Transversal
VocabularyWrite the term from the box that best completes each sentence.
transversal alternate interior angles alternate exterior angles
same-side interior angles same-side exterior angles
1. 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 is a line that intersects two or more lines.
3. 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. 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. 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 in
between the other two lines.
Lesson 10.3 Skills Practice
Name ________________________________________________________ Date _________________________
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Lesson 10.3 Skills Practice page 2
Problem SetSketch an example of each.
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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Lesson 10.3 Skills Practice page 3
Name ________________________________________________________ Date _________________________
Use the map to give an example of each type of relationship.
1
23
5
4
67
9
8
10
11
23 24
25 26
27 28
29 30
19
222120
1516
1718
12
13 14
Taylor Ave
Hoo
ver
Ave
Wils
onA
ve
Roosevelt Ave
Monroe Dr
Polk Way
7. transversal
Hoover Ave. is a transversal that
intersects Monroe Dr. and Polk Way.
8. alternate interior angles
9. alternate exterior angles 10. same-side interior angles
11. same-side exterior 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
are congruent .
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°152°
152°152°
28°
28°
28°28°
18.
4x°
x°
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Lesson 10.3 Skills Practice page 5
Name ________________________________________________________ Date _________________________
19.
x°x° � 20
20.
75°�1
�2
�4�3
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Lesson 10.3 Skills Practice page 6
21. Solve for the value of x and y
given that ℓ1 ℓ2.
x°
y°
�1
�2
66°
22. Solve for the value of x given
that ℓ1 ℓ2.
x° 55°
125°
�1 �2
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Parallel or Perpendicular?Slopes of Parallel and Perpendicular Lines
VocabularyDefine each term in your own words.
1. Reciprocal
2. Negative reciprocal
Problem SetDetermine 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
slope of a line parallel to it is 6.
2. y 5 2 __ 3
x 2 5
3. y 5 8 2 5x 4. y 5 14 2 1 __ 4
x
Lesson 10.4 Skills Practice
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Lesson 10.4 Skills Practice page 2
5. 3x 1 4y 5 24 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 c. y 5 4 1 8x
slope 5 8 slope 528 slope 5 8
The equations (a) and (c) represent parallel lines.
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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Lesson 10.4 Skills Practice page 3
Name ________________________________________________________ Date _________________________
10. a. 4y 5 4x 2 16 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
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Lesson 10.4 Skills Practice page 4
12. a. 2x 1 8y 5 24 b. 232x 1 4y 5 12 c. 240x 1 5y 5 10
Determine the negative reciprocal of each number.
13. 5
2 1 __ 5
14. 27 15. 3 __ 4
16. 2 5
__ 8 17. 1 __ 7
18. 2 2 __ 5
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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
The slope of the line is 13, so the slope
of a line perpendicular to it is 2 1 ___ 13 .
20. y 5 5x 2 17
21. y 5 1 __ 6
x 1 4 22. y 5 9 2 1 __ 3
x
23. 5x 1 6y 5 36 24. 4x 2 3y 5 21
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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 __ 3
x 2 8 b. y 5 3 __ 2 x 2 1 c. y 5 2 3 __
2 x 1 14
slope 5 2 __ 3
slope 5 3 __ 2
slope 52 3 __ 2
The equations (a) and (c) represent perpendicular lines.
26. a. y 5 25x 2 23 b. y 5 18 1 1 __ 5
x 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
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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
29. a. 26x 1 2y 5 20 b. 29x 2 3y 5 218 c. x 1 3y 5 15
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Lesson 10.4 Skills Practice page 8
30. a. 3x 1 18y 5 272 b. 30x 1 5y 5 25 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
The slopes are equal, so the lines are parallel.
32. y 5 15 2 2x y 5 1 __ 2
x 1 17
33. y 5 1 __ 3
x 1 5 y 5 3x 2 2
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Lesson 10.4 Skills Practice page 9
Name ________________________________________________________ Date _________________________
34. 3x 1 12y 5 24 220x 1 5y 5 40
35. 3x 1 2y 5 2 2x 1 3y 5 3
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Lesson 10.4 Skills Practice page 10
36. 10y 5 6x 1 80 212x 1 20y 5 160
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Up, Down, and All AroundLine Transformations
VocabularyWrite a definition for the term in your own words.
1. Triangle Sum Theorem
Problem SetSketch 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.
A
B
C
D
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 3 2 1 ______ 6 2 2
5 2 __ 4
line CD: m 5 y2 2 y1 _______ x2 2 x1
5 7 2 5 ______ 6 2 2
5 2 __ 4
Line AB is parallel to line CD.
Lesson 10.5 Skills Practice
Name ________________________________________________________ Date _________________________
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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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
3. Horizontally translate line AB 25 units to create line CD. Calculate the slope of each line to
determine if the lines are parallel.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8A
B
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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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
5. Vertically translate line AB 7 units to create line CD. Calculate the slope of each line to determine if
the lines are parallel.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
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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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
C B
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 5 2 3 ______ 5 2 2
5 2 __ 3
line AC: m 5 y2 2 y1 _______ x2 2 x1
5 6 2 3 ______ 0 2 2
5 2 3 __ 2
Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other.
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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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8A
B
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.
A
B
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
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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.
x
y
–8
–6
–4
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
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.
A
B
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
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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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
C
D
E
F
G
H
slope of ___
AB 5 2 __ 5
slope of ___
EF 5 2 __ 5
___
AB ___
EF
slope of ___
CD 5 5 __ 2
slope of ____
GH 5 5 __ 2
___
CD ____
GH
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Lesson 10.5 Skills Practice page 8
14.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
AE
FB
15.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
E
F
16.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
B
A
F
E
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Lesson 10.5 Skills Practice page 9
Name ________________________________________________________ Date _________________________
17.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
B
AF
E
18.
B
A
F
E
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
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