Download Chapter 3 Answers

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Chapter 3 Answers
Practice 3-1
Practice 3-4
1. corresponding angles
2. alternate interior angles
3. same-side interior angles
4. alternate interior angles
5. same-side interior angles
6. corresponding angles
7. 1 and 5, 2 and 6, 3 and 8, 4 and 7
8. 4 and 6, 3 and 5
9. 4 and 5, 3 and 6
10. m1 = 100, alternate interior angles; m2 = 100,
corresponding angles or vertical angles
11. m1 = 75,
1. 125
2. 69
3. 143
4. 129
5. 140
6. 136
7. x = 35; y = 145; z = 25
8. a = 55; b = 97; c = 83
9. v = 118; w = 37; t = 62
10. 50
11. 88
12. m3 = 22; m4 = 22; m5 = 88
13. 57.1
14. 136
15. m1 = 33; m2 = 52
16. isosceles
17. obtuse scalene
18. right scalene
19. obtuse
isosceles
20. equiangular equilateral
alternate interior angles; m2 = 75, vertical angles or
corresponding angles
12. m1 = 135, corresponding
angles; m2 = 135, vertical angles
13. x = 103; 77°, 103°
14. x = 24; 12°, 168°
15. x = 30; 85°, 85°
16a. Alternate Interior Angles Theorem
16b. Vertical
angles are congruent.
16c. Transitive Property of
Congruence
Practice 3-2
* )
* )
1a. same-side interior
1b. QR
1c. TS
1d. * same-side
interior
1e.
Same-Side
Interior Angles
)
1f. TS
1g. 3-5
2. l and m, Converse of Same-Side
Interior Angles Theorem
3. none
4. BC and AD ,
Converse of Same-Side Interior Angles Theorem
5. RT
and HU , Converse of Corresponding Angles Postulate
6. BH and CI, Converse of Corresponding Angles Postulate
7. a and b, Converse of Same-Side Interior Angles Theorem
8. 43
9. 90
10. 38
11. 100
12. 70
13. 48
Practice 3-5
1. x = 120; y = 60
2. n = 5137
3. a = 108; b = 72
4. 109
5. 133
6. 129
7. 129
8. 47
9. 127
10. 30
11. 150
12. 6
13. 5
14. 8
15. BEDC
16. FAE
17. FAE and BAE
18. ABCDE
19. 20
Practice 3-6
1. y = 13 x - 7
4. y
9.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
= 16 x - 23
y
6
4
2
y 4x 1
2 4 6 x
y 1 x 2
3
2 4 6 x
–6–4–2
–2
–4
–6 y 1 x 5
4
x
4
2
–6–4 –2
–2
–4
–6
2 4 6 x
–6–4–2
–4
–6
y
15.
6
4
2
2 4 6
6 y 2x 7
4
2
–6–4 –2
–2
–4
–6
y yx1
12.
y
6
4
2
–6–4–2
–2
–4
–6
13.
6. y = 45 x - 2
10.
–6
11.
3. y = 7x - 18
8. y = -x + 6
y
6
4
2
–6–4–2
–2
l2
5. y
3
7. y = 4x - 13
Practice 3-3
1. True. Every avenue will be parallel to Founders Avenue, and
therefore every avenue will be perpendicular to Center City
Boulevard, and therefore every avenue will be perpendicular
to any street that is parallel to Center City Boulevard.
2. Not necessarily true. No information has been given about
the spacing of the streets.
3. True. The fact that one
intersection is perpendicular, plus the fact that every street
belongs to one of two groups of parallel streets, is enough to
guarantee that all intersections are perpendicular.
4. True.
Opposite sides of each block must be of the same type (avenue
or boulevard), and adjacent sides must be of opposite type.
5. Not necessarily true. If there are more than three avenues
and more than three boulevards, there will be some blocks
bordered by neither Center City Boulevard nor Founders
Avenue.
6. a ⊥ e
7. a || e
8. a || e
9. a ⊥ e
10. a ⊥ e
11. a || e
12. If the number of ⊥ statements is
even, then 1 || n. If it is odd, then 1 ⊥ n.
13. The proof
can instead use alternate interior angles or alternate exterior
angles (if the angles are congruent, the lines are parallel) or
same-side interior or same-side exterior angles (if the angles
are supplementary, the lines are parallel).
14. It is possible.
2. y = -2x + 12
1
= -2 x -
14.
2 4 6 x
y
6 y 2x 3
4
2
–6–4–2
–2
y
16.
y 3x 5
2 4 6 x
y
2
6 y x2
3
4
4
x
2 4 6
–6
–2
–2
–4
–6
2 4 6 x
l1
l3
Geometry Chapter 3
Answers
39
Chapter 3 Answers
2 4 6 x
–6–4–2
20.
y
6
4
2
x 2
–6–4
2 4 6 x
–2
–4
–6
21.
22.
y
–4
–6
2 4 6 x
y
23.
y
6
4
2
y – 3x 2 2
–6–4–2
–2
–4
–6
yx
2 4 6 x
–4
–6
24.
2 4 6 x
x 2.5
2 4 6 x
–6–4–2
–2
–4
–6
25. y = –3x + 13
26. y = x + 4
27. y = 21 x - 3
1
1
28. y = -2 x - 2
29. y = 2x + 4
30. y = 13 x + 4
31. y = -51 x - 65
32. y = -6x + 45
33. x = 2;
y = -11
34. x = 0; y = 2
35. x = -4; y = -4
36. x = -1; y = 8
37.
y
6
4 (4, 0)
2
38.
y
(–2, 0) 6
4
2
6 x
–6–4–2 2
–2
–4
–6
–8
–10
–12 (0, 12)
–6 –4–2
–2
(0, 6)
(9, 0)
x
2 4 6 8
–4
–6
–2
–2 2 4 6 x
–4
–6
45a. m = $0.10
45b. the amount of money the worker is
paid for each box loaded onto the truck
45c. b = $3.90
45d. the base amount the worker is paid per hour
46. y = -25 x + 8
Practice 3-7
y
6
4
2
2 4 6 8 x
y
6
4
2
6
4
(–3, 0) 2
–6
–6–4–2
y 5
44.
12 (0, 12)
10
6
4
2
2 4 6 x
–6–4–2
–2
–6–4–2
–2
–4
–6
y
6
4
–6–4–2
–2
–4
–6
6
4
2
y
6
4
2 (0, 1) (8, 0)
2 4 6 x
–6–4–2
–2
–4 (0, –4)
–6
43.
y
y 2x
42.
y
6
4
2 (4, 0)
6x
–6–4–2
2
–2
1
–4 y 2 x 3
–6
–4
–6
19.
41.
y
6
4
2
–6 –4 –2 2 4 6 x
–2
–4
–6 (0, –1)
1. neither; 3 2 31, 3 ? 31 2 -1
2. perpendicular;
1
2
?
2
=
1
3.
parallel;
=
-23
4. parallel;
2
3
-1 = -1
5. perpendicular; y = 2 is a horizontal line,
x = 0 is a vertical line
6. parallel; -12 = -12
7. neither; 1 2 81, 1 ? 18 2 -1
8. parallel; -23 = -23
9. perpendicular; -1 ? 1 = -1
10. neither; 21 2
5 1
5
7
7
2
-3, 2 ? –3 2 -1
11. neither; -3 2 -12
, -23 ? -12
2 -1
1
1
12. neither; 6 2 -5, 6 ? -5 2 -1
13. neither; 29 2 4, 92 ? 4 2 -1
14. parallel; 21 = 12
15. y = 32 x
4
16. y = -3 x + 24
y
17. y = -x - 3
6
4
18. y = 35 x + 6
2
19. y = 0
–6–4 L
4 6 x
20. y = 2x - 4
–4
21. y = 2x
Practice 3-8
1.–3.
4.–6.
Q
39.
y
6 (0, 6)
4
2
–6–4–2
–2
–4
–6
40
2 4 6 x
(6, 0)
Answers
40.
y
6
4
1
(– 2, 0) 2 (0, 2)
–6–4–2
All rights reserved.
18.
y
6
4 y 5x 4
2
T
2 4 6 x
–4
–6
Geometry Chapter 3
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
17.
(continued)
Chapter 3 Answers
(continued)
14. Sample:
7.–9.
K
b
c
10. Sample:
15.
All rights reserved.
b
a
a
11. Sample:
a
b
Reteaching 3-1
1a.–1b. Sample:
c
60
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
12.
1c.–1d. Sample:
b
b
120 60
60 120
b
120 60
60 120
b
2. 110
7. 70
3. 70
8. 110
4. 110
5. 110
6. 70
Reteaching 3-2
13.
1.
l6m
1 3
Given
If 6 lines, then
corresponding s are .
a
m3 = m2 = 180
Substitution
c
2 and 3 are
supplementary.
Definition of
supplementary
m1 + m2 = 180
Angle Addition Postulate
Geometry Chapter 3
Answers
41
(continued)
2. 2 3
Given
3 1
a6b
Substitution If corresponding s,
then lines are parallel.
2 1
Vertical s are .
15. y = 14 x + 21
17. y = -x + 1
Reteaching 3-7
1a. -2
1b. 12
2a. 14
3b. 0
4a. y = -2x + 4
4c.
2b. -4
3a. undefined
4b. y = 12 x + 32
y
Reteaching 3-3
1. Draw a temporary line through A that is perpendicular to ,
then draw a second, permanent line through A that is
perpendicular to the first. This line will be parallel to . Repeat
for B. The two permanent lines will be parallel not only to but to each other (Theorem 3-9).
2. Draw two
perpendicular lines through C, then for each one draw a line
perpendicular to it that runs through D. The four lines will
define a rectangle.
3. Draw a line that runs through both E
and F, and then a second line at an acute or obtuse angle that
runs through E. Draw a third line, parallel to the second and
running through F, using the same procedure as in the Example
and in Exercise 1. In the same way, draw a fourth line parallel to
the first (at any desired distance from it). The four lines will
define a parallelogram.
16. y = -34 x + 4
18. y = 1
4
2
2
O
2
4
x
All rights reserved.
Chapter 3 Answers
2
4
5b. y = 32 x - 4
5a. y = -32 x - 4
5c.
y
4
Reteaching 3-4
2
1. ABD: mABD = 120, mADB = 30; CBE:
4
m3 = 60; m4 = 120
2
4
x
2
4
6a. y = 3x + 7
6c.
6b. y = -13 x - 3
y
4
2
Reteaching 3-5
1. 1 and 2 are interior angles; 3 and 4 are exterior
angles.
2. m1 = 135; m2 = 90; m3 = 45;
m4 = 90
3. 1 is an interior angle; 2 and 4 are
exterior angles; 3 is neither.
4. m1 = 60; m2 = 120;
2 O
4
2 O
2
4
x
2
4
Reteaching 3-6
Check students’ graphs.
1. y = 2x - 6
2. y = 13 x
3. y = -x - 3
5
4. y = 6 x + 2
5. y = -12 x + 1
6. y = 1
7. y = -72 x + 10
8. y = -x + 1
9. y = 52 x + 1
10. y = 1
11. y = -2x - 6
12. x = -3
13. y = -3x + 10
14. y = 3x - 10
42
Answers
7. mJK = -1; mLM = -1; parallel
8. mJK = 32 ; mLM =
3
1
-2 ; perpendicular
9. mJK = -6; mLM = -15 ; neither
3
10. mJK = -2 ; mLM = 54; neither
11. mJK = 2; mLM =
1
1
-2; perpendicular
12. mJK = 5; mLM = 5; neither
13. mJK = 14; mLM = -14; parallel
14. mJK undefined;
mLM = 0; perpendicular
Geometry Chapter 3
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
mCBE = 120, mCEB = 30, mBCE = 30; BDE:
mBDE = 60, mDBE = 60, mBED = 60
2. DBE and ABC are acute, equiangular, and
equilateral; ABD and CBE are isosceles and obtuse;
ACE, ADE, CED, and CAD are right and scalene.
3. PQT: mPTQ = 45, mPQT = 90; PQR:
mPQR = 90, mQPR = 45, mQRP = 45; RQS:
mRQS = 90, mQSR = 45; SQT: mSQT = 90,
mQST = 45, mSTQ = 45
4. PT = TS = RS =
PR = 40 mm; PQ = QT = QR = QS = 28 mm
5. PQT, PQR, RQS, SQT, PRS, PTS, PRT,
and RST are right and isosceles.
Chapter 3 Answers
(continued)
8. Figures A and B
ones, with precise control of the slant.
would be easy, because the lines have no more than two or
three different slants. Figure C would be harder, because lots
of different slants are used to achieve the perspective effect.
Reteaching 3-8
1. Sample:
Z
Enrichment 3-4
b
X
a
1. 48
2. 2880
3. 4320
4. Angles have measures of
20, 70, or 90; AC 6 MD 6 LE 6 KF 6 JG; BM6 CH 6 NK;
AH 6 PG; CM 6 DL 6 EK 6 JF 6 IG.
Y
Enrichment 3-5
All rights reserved.
1. 2
2. 5
7. Number
2.–4. Check students’ work.
Enrichment
)
* 3-1
)
1. OE * is #) to AB .
2. 3, 5, 1, 4, 2, 6 or 4, 5, 1, 3, 2, 6; OE
)
is # to AB ; if two angles are congruent and supplementary,
then each measures 90°.
3. 1 > 2; Law of Reflection
4. 2 > 3; Alternate Interior Angles Theorem
5. 3 > 4; Law of Reflection
6. 1 > 4; Transitive
Property of Congruence
3. 9
1.–8.
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y
3
1
5 A
4
T
2
D
3. 33
4. 41
Enrichment 3-3
1. If the paper shifts during drawing, lines meant to be parallel
will not be parallel, and lines meant to be perpendicular will
not be perpendicular.
2. The rectangular shape gives the
T-square two perpendicular guide edges on which to line up.
3. Theorem 3-10, which says that if two lines are perpendicular
to the same line, they are parallel to each other. A line drawn
with the T-square is perpendicular to the edge on which the Tsquare is lined up. Two lines drawn with the T-square lined up
on the same edge will be parallel to each other.
4. a ⊥ d. If the T-square is used to draw a line perpendicular to
a vertical edge of the rectangular backing surface, and then is
used to draw a line perpendicular to a horizontal edge of the
backing surface, then the two lines will be perpendicular.
5. Figure A would be easy; all the lines are parallel or
perpendicular. Figures B and C would be hard to draw, since
the lines are not all parallel or perpendicular to each other.
6. They will all be parallel to .
7. A drafting machine can
be used to draw slanted lines, not just vertical and horizontal
6
L
5. Sample:
H
Because mBAC = 41, mCAF = 180 - 41 = 139;
l 6 m because a pair of alternate interior angles are congruent.
6. CD and EF ; AK
7. Sample: CAB and IGH are
corresponding angles related to parallel segments AB and GH .
AK is the related transversal.
8. Sample: A, ADE,
and AED form a triangle, so 180 - (43 + 76) = 61, so
mAED = 61. Because AED and C are congruent
corresponding angles, DE 6 BC by the Converse of the
Corresponding Angles Postulate.
Geometry Chapter 3
6. 27
Enrichment 3-6
Enrichment 3-2
2. 106
5. 20
3
4
5
6
7
8
9
...
n
of sides
Total
180 360 540 720 900 1080 1260
(n 2)180
degree
measure
Number of
n(n 3)
0
2
5
9 14 20 27
2
diagonals
8
1. x = 11
4. 14
N
B
M
x
E
K
Y
P
C
S
7
R
RENE DESCARTES
Enrichment 3-7
1. (-3, 4)
2. (-2, 3)
3. (3, 3)
4. (-2, -2)
5. (-1, -1)
6. (4, -1)
7. (1, 0)
8. (2, -3)
9. (-1, 2)
10. (1, -4)
11. (-3, -3)
12. (2, 3)
13. (3, -2)
14. (5, 0)
15. (0, 1)
16. (4, 3)
y-axis
4
A
3
N
2
G
1
L
0
1
E
2
N
I
3
4 L
4 3 2 1 0
R
A
Y
E
T
N
I
O
P
1
2
3
4
Answers
5 x-axis
43
Chapter 3 Answers
(continued)
pentagons
Enrichment 3-8
1., 3., and 4.
hexagons
A
C
2. scalene, acute triangle
All rights reserved.
B
Activity 3: Analyzing
5. No; refer to the answer to
Exercises 1, 3, and 4.
6.
E
Activity 4: Modeling
F
7. isosceles, obtuse triangle
Chapter Project
Activity 1: Paper Folding
5; all triangles are right isosceles; yes.
Activity 2: Exploring
triangle
✔ Checkpoint Quiz 1
1. Converse of Corresponding Angles Postulate
2. Alternate Interior Angle Theorem
3. Same-Side
Interior Angles Theorem
4. Corresponding Angles
Postulate
5. Converse of Alternate Interior Angle
Theorem
6. Vertical Angles Theorem
7. Converse
of Corresponding Angles Postulate
8. Corresponding
Angles Postulate
9. Converse of Same-Side Interior
Angles Theorem
10. x = 50, y = 30, z = 65
✔ Checkpoint Quiz 2
1. pentagon; 80
2. hexagon; x = 110; y = 98
3. quadrilateral; x = 94; y = 105
y
y
4.
5.
quadrilaterals
8
6
4
2
(2,0)
4 6 8 x
8642
2 2
4
6
8 (0,8)
44
Answers
8
6
4 (0,3)
(1.2,0) 2
2 4 6 8 x
8642
2
4
6
8
Geometry Chapter 3
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
D
Chapter 3 Answers
(continued)
y
6.
Chapter Test, Form B
8
6
4
2
42
2
4
6
8
1. true 2. true 3. false 4. true 5. false
6. m1 = 62, m2 = 62, alternate interior angles
7. m1 = 85, m2 = 95, same-side interior angles
8. m1 = 75, m2 = 75, alternate interior angles
y
y
9.
10.
(12,0)
2 4 6 8 10 12 x
(0,8)
7. Parallel; slopes are the same.
8. neither
9. Perpendicular; the product of the slopes is -1.
10. neither
Chapter Test, Form A
All rights reserved.
1. true
6. false
2. true
7. true
3. false
8. true
4. false
5. true
9. Answers may vary.
Sample: m1 = 125, Same-Side Interior Angles Theorem; m2
= 55, Alternate Interior Angles Theorem
10. Answers may
vary. Sample: m1 = 60, Corresponding Angles Postulate then
Angle Addition Postulate; m2 = 60, Same-Side Interior
11. Answers may vary. Sample: m1 = 85,
Angles Theorem
Alternate Interior Angles Theorem; m2 = 95, Same-Side
12. Answers may vary. Sample:
Interior Angles Theorem
m1 = 75, Corresponding Angles Postulate; m2 = 105,
13. Answers may vary. Sample:
Angle Addition Postulate
m1 = 91, Corresponding Angles Postulate and Same-Side
Interior Angles Theorem; m2 = 89, Corresponding Angles
14. Answers may vary. Sample: m1 = 60,
Postulate
Alternate Interior Angles Theorem; m2 = 115, Same-Side
Interior Angles Theorem
15.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
X
4
4
4
2
2
2
2
4 x
2
2
4 x
4
4
11. AD and WZ 12. AD and WZ 13. AD and WZ
14. AW and DZ 15. x = 92, y = 88 16. w = 31,
x = 65, y = 65, z = 115 17. 1440 18. 45
19. neither 20. perpendicular 21. parallel
22. y = 3x - 1 23. y = 14 x - 3 24. y = -2x - 2
Alternative Assessment, Form C
TASK 1: Scoring Guide
a.
t
1 2
4 3
5 8
6 7
a
b
b. Sample: 8 2; 8 4; 8 and 3 are
supplementary.
c. m2 = 75; m3 = 105, m4 = 75,
m5 = 105, m6 = 75, m7 = 105, m8 = 75
m
d. 7 and 4 are supp.
Given
16.
x
4 8
a6b
Supp. of the
same are .
If alt. int s
are , then
lines are 6.
7 and 8 are supp.
y
17. WA and XB
18. none
19. WZ and AB
20. none
21. WZ and AB
22. WZ and AB; AX
and BY
23. x = 22; y = 120
24. x = 70; y = 60;
z = 120
25. x = 35; y = 35; z = 55
26. 5940
27. 18
28. perpendicular
29. neither
30. parallel
31. y = 6x + 23
32. y = -21 x + 3
33. y = 13 x + 2
Geometry Chapter 3
Angle Add. Post.
3 Student draws an accurate diagram and supplies correct
answers and a complete and accurate flow proof.
2 Student draws a figure or gives answers that contain
minor errors.
1 Student draws a figure or gives answers that contain
significant errors or omissions.
0 Student makes little or no attempt.
Answers
45
(continued)
TASK 2: Scoring Guide
TASK 4: Scoring Guide
Sample:
Sample:
Q
A
P
Isosceles
Triangles
B
Equilateral
Triangles
3 Student constructs an accurate figure.
2 Student constructs a figure that contains minor errors
or omissions.
1 Student constructs a figure that contains significant errors
or omissions.
0 Student makes little or no attempt.
TASK 3: Scoring Guide
Sample:
Triangles
R
3 Student draws an accurate diagram.
2 Student draws a diagram that contains minor errors
or omissions.
1 Student draws a diagram that contains significant errors
or omissions.
0 Student makes little or no attempt.
All rights reserved.
Chapter 3 Answers
Cumulative Review
B
A
D
C
1. D
2. G
3. C
4. F
5. D
6. J
7. A
8. F
9. C
10. H
11. D
12. J
13. B
14. G
15. C
16. G
17. C
18. Given
19. Same-Side Interior Angles Theorem
20. Corresponding Angles Postulate
21. Corresponding
Angles Postulate
22. substitution
23. Check students’
work.
24. Sketches may vary. The right angle must be
between the equal sides.
25. No; a triangle cannot have
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
two sides equal and no sides equal at the same time.
a. For the figure given, y = x and y = x + 3. The lines are
parallel because both lines have a slope of 1.
c. For ABC, the sum of the three angles is 180°. Minor
discrepancies are the result of measurement error and
rounding error.
d. For the figure given, ABDC is not regular. By the
distance formula, the sides are not congruent.
3 Student draws the figure accurately, writes correct equations,
and reasons logically.
2 Student draws a figure, gives arguments, and writes
equations that are mainly correct but may contain minor
errors.
1 Student presents work with significant errors.
0 Student makes little or no attempt.
46
Answers
Geometry Chapter 3