Location, Location, Location! - rcsdk8.org 10 Skills...Chapter 10 Skills Practice • 711 © 2011...
Transcript of Location, Location, Location! - rcsdk8.org 10 Skills...Chapter 10 Skills Practice • 711 © 2011...
Chapter 10 Skills Practice • 711
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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. Parallel lines are lines that lie in the same plane and do not intersect.
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
when they are graphed.
4. Perpendicular lines are lines that intersect at a right angle.
5. Skew lines are lines that do not lie in the same plane.
6. Coplanar lines 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.
parallel lines, coplanar lines
Lesson 10.1 Skills Practice
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Lesson 10.1 Skills Practice page 2
3.
coplanar lines, intersecting lines
4.
coincidental lines, coplanar lines
5.
skew lines
6.
intersecting lines, coplanar lines
Sketch an example of each relationship.
Answers will vary.
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.
Case 1
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Lesson 10.1 Skills Practice page 4
15.
Case 3
16.
Case 1
17.
Case 4
18.
Case 3
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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
Answers will vary.
Magnolia Drive and Cherry Street
21. parallel lines
Answers will vary.
Cherry Street and Chestnut Street
22. skew lines
None. All streets are in the same plane.
23. coincidental lines
North Daisy Lane and South Daisy Lane
24. coplanar lines
Answers will vary.
All streets are in the same plane.
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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
b. linear pair of angles
a. supplementary angles
2. Two angles whose sum is 180 degrees
a. supplementary angles
b. linear pair of angles
Problem SetSketch an example of each relationship.
Answers will vary.
1. congruent figures 2. congruent angles
30° 30°
3. adjacent angles 4. vertical angles
60°60°
Lesson 10.2 Skills Practice
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Lesson 10.2 Skills Practice page 2
5. linear pair
140°
40°
6. supplementary angles
145°
35°
Use the map to give an example of each relationship.
Answers will vary.
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
2 and 5
9. supplementary angles
9 and 10
10. linear pair
11 and 12
11. adjacent angles
17 and 18
12. vertical angles
12 and 17
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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°
16. Draw 2 adjacent to 1.
12
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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.
1
2
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?
m1 1 m2 5 180
101 1 x 5 180
x 5 79
m2 5 79°
21. If 1 and 2 form a linear pair and m1 is one-fifth m2, what is the measure of each angle?
m1 1 m2 5 180
0.2x 1 x 5 180
1.2x 5 180
x 5 150 and 0.2x 5 0.2(150) 5 30
m2 5 150° and m1 5 30°
22. If 1 and 2 are supplementary angles and m1 is 60° less than m2, what is the measure of
each angle?
m1 1 m2 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
m2 5 120° and m1 5 60°
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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?
m1 1 m2 5 180
3x 1 x 5 180
4x 5 180
x 5 45 and 3x 5 3(45) 5 135
m2 5 45° and m1 5 135°
24. If 1 and 2 are supplementary angles and m1 is 12° more than m2, what is the measure of
each angle?
m1 1 m2 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
m2 5 84° and m1 5 96°
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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. 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 transversal is a line that intersects two or more lines.
3. Same-side exterior angles 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)
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
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Lesson 10.3 Skills Practice page 2
Problem SetSketch an example of each.
Answers will vary.
1. Transversal 2. Alternate interior angles
12
3. Alternate exterior angles
1 2
4. Same-side interior angles
12
5. Same-side exterior angles
1
2
6. Corresponding angles
12
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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.
Answers will vary.
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
8 and 5
9. alternate exterior angles
11 and 18
10. same-side interior angles
12 and 15
11. same-side exterior angles
18 and 13
12. corresponding angles
24 and 28
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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 supplementary .
15. The alternate exterior angles formed when two parallel lines are intersected by a transversal
are congruent .
16. The same-side exterior angles formed when two parallel lines are intersected by a transversal
are supplementary .
Determine the measure of all the angles in each.
17.
152°152°
152°152°
28°
28°
28°28°
18.
4x°
x°36°
36°
36°
36°
144°
144°
144°
144°
x 1 4x 5 180
5x 5 180
x 5 36
4x 5 144
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Lesson 10.3 Skills Practice page 5
Name ________________________________________________________ Date _________________________
19.
x°x° � 2080°
80° 100°
80°
100°
100°
80°100°
x 2 20 1 x 5 180
2x 2 20 5 180
2x 5 200
x 5 100
x 2 20 5 80
20.
75°�1
�2
�4�3
75° 75°75°
75°
105°105°
105°105°105°
105°105°
75°
75°
75°105°
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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
�266°
66°66°
66°
66 1 90 1 y 5 180
y 5 24
66 1 90 1 x 5 180
x 5 24
22. Solve for the value of x given
that ℓ1 ℓ2.
x° 55°
125°
55°55°
�1 �2
110°
70°
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Parallel or Perpendicular?Slopes of Parallel and Perpendicular Lines
VocabularyDefine 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 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
The slope of the line is 2 __ 3 , so the
slope of a line parallel to it is 2 __ 3
.
3. y 5 8 2 5x
The slope of the line is 25, so the
slope of a line parallel to it is 25.
4. y 5 14 2 1 __ 4
x
The slope of the line is 21 __ 4
, so the
slope of a line parallel to it is 21 __ 4
.
Lesson 10.4 Skills Practice
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Lesson 10.4 Skills Practice page 2
5. 3x 1 4y 5 24
3x 1 4y 5 24
4y 5 24 23x
y 5 6 2 3 __ 4
x
The slope of the line is 23 __ 4 , so the
slope of a line parallel to it is 23 __ 4 .
6. 15x 2 5y 5 40
15x 2 5y 5 40
25y 5 40 215x
y 5 28 1 3x
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 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
slope 523 slope 523 slope 53
The equations (a) and (b) represent parallel lines.
9. a. 5y 5 220x 2 45 b. 2y 5 4x 1 6 c. 4y 5 32 2 16x
5y 5220x 2 45 2y 54x 1 6 4y 532 2 16x
y 524x 2 9 y 52x 1 3 y 58 2 4x
slope 524 slope 52 slope 524
The equations (a) and (c) represent parallel lines.
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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
4y 54x 2 16 2y 58 1 4x 3y 56x 1 18
y 5x 2 4 y 54 1 2x y 52x 1 6
slope 51 slope 52 slope 52
The equations (b) and (c) represent parallel lines.
11. a. 3x 1 5y 5 60 b. 6x 1 10y 5 240 c. 15x 1 9y 5 18
3x 1 5y 5 60 6x 1 10y 5240 15x 1 9y 5 18
5y 523x 1 60 10y 526x 2 40 9y 5215x 1 18
y 52 3 __ 5 x 1 12 y 52 6 ___
10 x 2 4 y 52 15 ___
9 x 1 2
slope 52 3 __ 5 y 52 3 __
5 x 2 4 y 52 5 __
3 x 1 2
slope 52 3 __ 5
slope 52 5 __ 3
The equations (a) and (b) represent parallel lines.
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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
2x 1 8y 5 24 232x 1 4y 512 240x 1 5y 5 10
8y 5x 1 24 4y 532x 1 12 5y 540x 1 10
y 5 1 __ 8 x 1 3 y 58x 1 3 y 58x 1 2
slope 5 1 __ 8 slope 58 slope 58
The equations (b) and (c) represent parallel lines.
Determine the negative reciprocal of each number.
13. 5
2 1 __ 5
14. 27
1 __ 7
15. 3 __ 4
2 4 __ 3
16. 2 5
__ 8
8 __ 5
17. 1 __ 7
27
18. 2 2 __ 5
5 __ 2
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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
The slope of the line is 5, so the slope of
a line perpendicular to it is 2 1 __ 5
.
21. y 5 1 __ 6
x 1 4
The slope of the line is 1 __ 6
, so the
slope of a line perpendicular to it is 26.
22. y 5 9 2 1 __ 3
x
The slope of the line is 2 1 __ 3
, so the
slope of a line perpendicular to it is 3.
23. 5x 1 6y 5 36
5x 1 6y 5 36
6y 525x 1 36
y 52 5 __ 6 x 1 6
The slope of the line is 2 5 __ 6 , so the
slope of a line perpendicular to it is 6 __ 5
.
24. 4x 2 3y 5 21
4x 2 3y 5 21
23y 524x 1 21
y 5 4 __ 3
x 2 7
The slope of the line is 4 __ 3 , so the
slope of a line perpendicular to it is 2 3 __ 4 .
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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
slope 525 slope 5 1 __ 5
slope 55
The equations (a) and (b) represent perpendicular lines.
27. a. 26y 5 24x 1 12 b. 2y 5 3x 1 8 c. 29y 5 6x 1 9
26y 524x 1 12 2y 53x 1 8 29y 56x 1 9
y 5 4 __ 6
x 2 2 y 5 3 __ 2
x 1 4 y 52 6 __ 9
x 2 1
y 5 2 __ 3
x 2 2 slope 5 3 __ 2
y 52 2 __ 3
x 2 1
slope 5 2 __ 3
slope 52 2 __ 3
The equations (b) and (c) represent perpendicular lines.
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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
25y 525x 1 55 5y 5x 1 15 4y 520x 2 24
y 525x 2 11 y 5 1 __ 5
x 1 3 y 55x 2 6
slope 525 slope 5 1 __ 5
slope 55
The equations (a) and (b) represent perpendicular lines.
29. a. 26x 1 2y 5 20 b. 29x 2 3y 5 218 c. x 1 3y 5 15
26x 12y 5 20 29x 23y 5218 x 13y 5 15
2y 56x 1 20 23y 59x 2 18 3y 52x 1 15
y 53x 1 10 y 523x 1 6 y 52 1 __ 3
x 1 5
slope 53 slope 523 slope 52 1 __ 3
The equations (a) and (c) represent perpendicular lines.
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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
3x 118y 5272 30x 15y 525 22x 112y 5224
18y 523x 2 72 5y 5230x 1 25 12y 52x 2 24
y 52 3 ___ 18 x 2 4 y 526x 1 5 y 5 2 ___ 12
x 2 2
y 52 1 __ 6
x 2 4 slope 526 y 5 1 __ 6
x 2 2
slope 52 1 __ 6
slope 5 1 __ 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 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
slope 522 slope 5 1 __ 2
The product of the slopes is 21, so the lines are perpendicular.
33. y 5 1 __ 3
x 1 5 y 5 3x 2 2
slope 5 1 __ 3
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.
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Lesson 10.4 Skills Practice page 9
Name ________________________________________________________ Date _________________________
34. 3x 1 12y 5 24 220x 1 5y 5 40
3x 112y 5 24 220x 15y 5 40
12y 523x 1 24 5y 520x 1 40
y 52 3 ___ 12
x 1 2 y 54x 1 8
y 52 1 __ 4 x 1 2 slope 54
slope 52 1 __ 4
The product of the slopes is 21, so the lines are perpendicular.
35. 3x 1 2y 5 2 2x 1 3y 5 3
3x 12y 5 2 2x 13y 5 3
2y 523x 1 2 3y 522x 1 3
y 52 3 __ 2 x 1 1 y 52 2 __
3 x 1 1
slope 52 3 __ 2 slope 52 2 __
3
The product of the slopes is not 21, and the slopes are not equal, so the lines are neither
parallel nor perpendicular.
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Lesson 10.4 Skills Practice page 10
36. 10y 5 6x 1 80 212x 1 20y 5 160
10y 56x 1 80 212x 120y 5 160
y 5 6 ___ 10
x 1 8 20y 512x 1 160
y 5 3 __ 5 x 1 8 y 5 12 ___
20 x 1 8
slope 5 3 __ 5 y 5 3 __
5 x 1 8
slope 5 3 __ 5
The slopes are equal, so the lines are parallel.
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Up, Down, and All AroundLine Transformations
VocabularyWrite 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 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
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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
D
C
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 8 2 5 ________ 3 2 (24)
5 3 __ 7
line CD: m 5 y2 2 y1 _______ x2 2 x1
5 0 2 (23)
________ 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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8A
BD
C
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 2 2 (21)
________ 2 2 (23)
5 3 __ 5
line CD: m 5 y2 2 y1 _______ x2 2 x1
5 2 2 (21)
__________ 23 2 (28)
5 3 __ 5
Line AB is parallel to line CD.
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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
BD
C
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 1 2 (25)
________ 1 2 (22)
5 6 __ 3
line CD: m 5 y2 2 y1 _______ x2 2 x1
5 1 2 (25)
________ 7 2 4
5 6 __ 3
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.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
D
C
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 24 2 1 ________ 2 2 (23)
5 25 ___ 5
line CD: m 5 y2 2 y1 _______ x2 2 x1
5 3 2 8 ________ 2 2 (23)
5 25 ___ 5
Line AB is parallel to line CD.
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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
BD
C
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 24 2 1 ________ 1 2 (21)
5 25 ___ 2
line CD: m 5 y2 2 y1 _______ x2 2 x1
5 24 2 1 __________ 22 2 (24)
5 25 ___ 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.
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
CB
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 4 2 0 ______ 3 2 1
5 4 __ 2
line BC: m 5 y2 2 y1 _______ x2 2 x1
5 4 2 6 ________ 3 2 (21)
5 22 __ 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.
A
C
B
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 23 2 1 ________ 1 2 (24)
5 2 4 __ 5
line AC: m 5 y2 2 y1 _______ x2 2 x1
5 6 2 1 ________ 0 2 (24)
5 5 __ 4
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 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
CB
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 22 2 3 __________ 21 2 (22)
5 2 5 __ 1
line BC: m 5 y2 2 y1 _______ x1 2 x1
5 22 2 (21)
__________ 21 2 4
5 1 __ 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.
A
C
B
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 6 2 2 __________ 21 2 (24)
5 4 __ 3
line AC: m 5 y2 2 y1 _______ x2 2 x1
5 21 2 2 ________ 0 2 (24)
5 2 3 __ 4
Line AB is perpendicular to line AC because the slopes are negative reciprocals of each other.
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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
C
B
line AB: m 5 y2 2 y1 _______ x2 2 x1
5 23 2 3 _______ 5 2 1
5 2 6 __ 4
line BC: m 5 y2 2 y1 _______ x2 2 x1
5 23 2 (27)
__________ 5 2 (21)
5 4 __ 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.
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
C
DG
H
slope of ___
AB 52 6 __ 2
slope of ___
EF 52 6 __ 2
___
AB ___
EF
slope of ___
CD 52 2 __ 6
slope of ____
GH 52 2 __ 6
___
CD ____
GH
15.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
A
B
C
D
G
H
E
F
slope of ___
AB 52 2 __ 6
slope of ___
EF 52 2 __ 6
___
AB ___
EF
slope of ___
CD 52 6 __ 2
slope of ____
GH 52 6 __ 2
___
CD ____
GH
16.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
B
D
C
H
G
A
F
E
slope of ___
AB 5 2 __ 6
slope of ___
EF 5 2 __ 6
___
AB ___
EF
slope of ___
CD 5 6 __ 2
slope of ____
GH 5 6 __ 2
___
CD ____
GH
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Name ________________________________________________________ Date _________________________
17.
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
B
C
G
D
H
AF
E
slope of ___
AB 52 3 __ 5
slope of ___
EF 52 3 __ 5
___
AB ___
EF
slope of ___
CD 52 5 __ 3
slope of ____
GH 52 5 __ 3
___
CD ____
GH
18.
B
C
D
G
H
A
F
E
x
y
–8
–6
–4
–2
2
4
6
8
–2–4 2 4 6–6–8 8
slope of ___
AB 5 5 __ 6
slope of ___
EF 5 5 __ 6
___
AB ___
EF
slope of ___
CD 5 6 __ 5
slope of ____
GH 5 6 __ 5
___
CD ____
GH