Post on 12-May-2018
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8 ANSWERS TO EXERCISES
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Answers to Exercises21. AB��, AC�� 22. PM��, PN��
23. XY��, XZ�� 24.
25. 26.
27.
28. 10
29–31.
32. Yes, P�(6, 2), Q�(5, �2), R�(4, �6); the slope
between any two of the points is �41
�.
33. possible answer:
34.
35. Answers will vary. Possible answers:
8 cm
11 cm
8 cm
11 cm
T
A
GY
R
y
x
N
P
Q
x
y
P
R
Q
R´
P´
Q´
y
xA (4, 0)
M
O
C
D
B
–5
–5
5
C
A BD
M
NX
Y
BA
CHAPTER 1 • CHAPTER CHAPTER 1 • CHAPTER
LESSON 1.1
1. sample answers: point: balls, where lines cross;
segment: lines of the parachute, court markings;
collinear: points along a line of the court structure;
coplanar: each boy’s hand, navel, and kneecap,
points along two strings
2. PT���, TP���3. any two of the following: AR���, RA���, AT���, TA���, RT���, TR���
4. any two of the following: MA���,MS���,AS���,AM���,SA���,SM���
5.6. 7.
8. AC� or CA� 9. PQ� or QP�
10. TR� or RT�, RI� or IR�, and TI� or IT�
11. 12.
13. mAB�� 14.3 cm 14. mCD�� 6.7 cm
15–17. Check each length to see if it is correct.
Refer to text for measurements.
18. R is the midpoint of PQ�. X is the midpoint of
WY��. Y is the midpoint of XZ�. No midpoints are
shown in �ABC.
19. possible answers:
20. P
Q
SM
T
orA C EDB
���� ����AC � CE
���� ����BC � CD
yS
R
x
11
BA
y
xD
E
–3
3
–3
3
K
L
BA
1
ANSWERS TO EXERCISES 9
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USING YOUR ALGEBRA SKILLS 1
1. (3, 4)
2. (�9, 1.5)
3. (5.5, 5.5)
4. (�6, 44)
5. Yes. The coordinates of the midpoint of a
segment with endpoints (a, b) and (c, d) are found
by taking the average of the x-coordinates, �a �
2c
�,
and the average of the y-coordinates, �b �
2d
�. Thus the
midpoint is ��a �2
c�, �
b �2
d��.
6. (3, 2) and (6, 4). To get the first point of
trisection, sum the coordinates of points A and B
to get (9, 6), then multiply those coordinates by �13
� to
get (3, 2). To get the second point of trisection, sum
the coordinates of points A and B to get (9, 6), then
multiply those coordinates by �23
� to get (6, 4). This
works because the coordinates of the first point
are (0, 0).
7. Find the midpoint, then find the midpoint of
each half.
8a. Midpoints for Figure 1 are (5.5, 6.5); for
Figure 2, (16, 6.75); and for Figure 3, (29.75, 5.5).
8b. For these figures the midpoints of the two
diagonals are the same point.
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LESSON 1.2
1. �TEN, �NET, �E; �FOU, �UOF, �1;
�ROU, �UOR, �2
2.
3.
4.
5. �S, �P, �R, �Q; none in the second figure
6. possible answer:
A
7. 90°
8. 120°
9. 45°
10. 135°
11. 45°
12. 135°
13. 30°
14. 90°
15. Yes; m�XQA � m�XQY � 45° � 90° � 135°,
which equals m�AQY.
16. 69°
17. 110°
18. 40°
19. 125°
20. 55°
21. �SML has the greater measure because
m�SML � 30° and m�BIG � 20°.
22.
23.
B90�
A44�
M
L
S
G
I
B
A T
N
24.
25.
26. no
27.
28.
29.
30. One possibility is 4:00.
31.
32.
33. G T
A
NI
R
T H
S A
T
H
O
90�
6 8
A
N
C
YD
A22�
22�
D
67.5�67.5�
C
D E
135�
B
C
D
ANSWERS TO EXERCISES 11
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34.
35. MY; CK; m�I 36. �SEU; �EUO; MO
37. x � 54° 38. y � 102°
39. z � 32° 40. 288°
41. 242° 42. They add to 360°.
43. no
44. You will miss the target because the incom-
ing angle is too big.
Target
Mirror
Laser lightsource
W
B OT
I
45. 180 km. The towns can be represented by
three collinear points, P, S, and G. Because S is
between P and G, PS � SG � PG.
46.
47.
48. MS � DG means that the distance between
M and S equals the distance between D and G.
MS � DG means that segment MS is congruent
to segment DG. The first statement equates two
numbers. The second statement concerns the
congruence between two geometric figures.
However, they convey the same information and
are marked the same way on a diagram.
49. Answers will vary. Possible answer.
70�40�
D E6 cm
F
70�40�
4 cmA B
C
4.36 cm
2.18 cm 2.18 cm
12 cm
6 cm 6 cm
12 ANSWERS TO EXERCISES
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LESSON 1.3
1–3. possible answers:
1.
2.
3.
4.
5.
6.
7.
8.
9. B is a Zoid. A Zoid is a creature that has in its
interior a small triangle with a large black dot
taking up most of its center.
10. A good definition places an object in a class
and also differentiates it from other objects in that
class. A good definition has no counterexamples.
D
40�
C
140�
A
40�
B
50�
EC
A D
B
P ER
A
M
S
D
G
I G
EB
T E
R
O G
D
45�
11. The measures of complementary angles sum
to 90°, whereas the measures of supplementary
angles sum to 180°.
12. No, supplementary angles can be uncon-
nected, while a linear pair must share a vertex and
a common side.
13a. an angle; measures less than 90°
13b. angles; have measures that add to 90°
13c. a point; divides a segment into two congruent
segments
13d. a geometry tool; is used to measure the sizes
of angles in degrees
14.
If AB��� and CD��� intersect at point P so that P is
between A and B, and P is between C and D, then
�APC and �BPD are a pair of vertical angles.
15. true
16. true
17. true
18. false
19. false
P
BC
D
A
ANSWERS TO EXERCISES 13
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20. false
21. true
22. false; Though the converse is true, a
counterexample is
23. false
24. false
25. possible answers: (�3, 0), (0, 2), or (6, 6)
26. possible answers: (2, �3) or (5, �1)
27. The reflected ray and the ray that passes
through (called the refracted ray) are mirror
images of each other. Or they form congruent
angles with the mirror.
B
A
Mirror
Reflectedsegment
C T
A
40�D
C140�
C T
A
50� 80�
50�
28. One possible answer is A(�8, 8), B(�4.5, 6.5),
C(�11, 1).
29. 12 cm
30. 36°
31. possible answer:
32.
33.
34a. �13
26
00
°°
� � �13
�, �23
� left
34b. �36600°°
� � �16
�, �16
� missing
34c. �36
90°� � 40°
1 pt.
4 pt.
5 pt. 6 pt.
2 pt.
3 pt.
Infinitelymany points
0 pt.
2 pt.
3 pt.
1 pt.
y
x–12 –6
A
B
C
T
S
R
6
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LESSON 1.4
1.
2. possible answers:
3.
4. octagon
5. hexagon
6. heptagon
7. pentagon
8–10. One possible answer for each is shown.
8. pentagon FIVER
9. quadrilateral FOUR
10. equilateral quadrilateral BLOC
11a. a polygon; has eight sides
11b. a polygon; has at least one diagonal outside
of the polygon
11c. a polygon; has 20 sides
11d. a polygon; has all sides of equal length
12. One possibility is �C and �Y are consecutive
angles; CY� and YN� are consecutive sides.
13. 9; possible answer:
14. AC�, AD��, BD�, BE�, CE�
15. �TIN
16. �WEN
17a. a � 44, b � 58, c � 34
17b. m�T � 87° and m�I � 165°
18. PA�� FI� and �IVE � �ANC
19. possible answer:
20. possible answer:
21. 84 in.
22. 5.25 cm
23. AB � 14 m, CD � 25 m
24. complementary angles: �AOS and �SOC;
vertical angles: �OCT and �ECR or �TCE and
�RCO
25.
26. possible answer:
27. All are possible except two points.
0 pts.
3 pts. 4 pts.
1 pt.
5 pts. 6 pts.
20
5
E
A B
C DF
130� 130�
5 cm
130�
ANSWERS TO EXERCISES 15
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LESSON 1.5
1. D 2. A
3. C 4. B
5. 6.
7.
8. possible answer:
9. possible answer:
10. possible answer:
11. possible answer:
12. possible answers: (�1, �1), (�1, 0), or (�4, 3)
13. possible answers: (3, �3), (3, 4), (�11, 4),
(�11, �3), (�0.5, 0.5), or (�7.5, 0.5)
14. possible answers: (�3, 1), (�1, �9), (2, 2),
(4, �8), (0, �1), or (1, �6)
15. possible answers:
9 cm45�
7 cm
BA
C
9 cm
12 cm
B
C
A45�
120�
4 cm
4 cm
ZP
A
80�4 cm
4 cm
BA
C
C
BA
C
BA6 cm 6 cm
40� 40�
b
2a2a
b – 2a
3a3a
R
A
C
S M L
C
A T
C
16. possible answers:
17. true
18. true
19. False, a diagonal connects nonconsecutive
vertices.
20. False, an angle bisector divides an angle into
two congruent angles.
21. true
22. (�4,1) → (�3,�2) (1,1) → (2, �2) (2, 4) →(3, 1) (�3, 5) → (�2, 2) Yes, the quadrilaterals are
congruent.
23. Find the midpoint of each rod. All the
midpoints lie on the same line; place the edge
of a ruler under this line.
24–26. Sample answers for 24–26
24. 25.
26. Q U
D A
P
AE
N T
P
AE
N T
y
(2, 4)
(1, 1)
(–3, 5)
(–4, 1)x
10 cm
40�
10 cm
E
F
A
10 cm
40�
14 cm
B
C
A
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LESSON 1.6
1. first figure: quadrilateral ABCD with two
congruent sides and one right angle; second
figure kite EFGH; third figure: trapezoid IJKL
with two right angles; fourth figure parallelogram
MNPQ
2. B 3. D
4. F 5. C
6. A, D, F
7.
8.
9.
10.
11.
12. square
13. possible answers: (2, 6), (�2, 4); (6, �2),
(2, �4); (3, �1), (1, 3)
14. 90 cm
15. (5, 6)
16. S(9, 0), I(4, �2)
17. S(�3, 0), I(�1, �5)
18. A(7, 6), N(5, 9) or A(�5, �2), N(�7, 1)
19a. Possible answer: Flip one triangle and align it
so that a congruent pair of sides forms a diagonal
of a kite.
T
R
H
G
I
E U
L
Q
A
N
BF
E
D I
Z O
19b. Possible answer: Rotate one triangle so that
a congruent pair of sides forms a diagonal of a
parallelogram.
20. There are three possibilities: a rhombus, a
concave kite, or a parallelogram.
21a. right triangles
21b. isosceles right triangles
22.
23.
24.
25. no
y
x
C (0, 5)
B (4, 4)
A (5, 0)
72�
72�
72�
72�
72�
5 cm5 cm
ANSWERS TO EXERCISES 17
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LESSON 1.7
1. Answers will vary. Sample answers:The green
area in the irrigation photo is a circle,the water is a
radius,and a path on the far side of the circle appears
to be tangent to the circle.The wood bridge is an arc of
a circle,and the railings are arcs of concentric circles.
The horizontal support beam under the bridge is
a chord.
2. three of the following: AB�, BD�, EC�, EF�
3. EC�
4. AP�, EP�, FP�, BP�, CP�
5. five of the following: EF�, AE�, AB�, BC�, CD�, DF�,
EB�, ED�, FC�, AC�, DB�, AF�, AD�, BF�
6. EDC� or EFC�, EBC� or EAC�
7. two of the following: ECD�, EDF�, FEC�, DEC�, . . .
8. FG���, HB���9. either F or B
10. possible answers: cars, trains, motorcycles;
washing machines, dishwashers, vacuum cleaners;
compact disc players, record players, car racing,
Ferris wheel
11. mPQ� � 110°; mPRQ� � 250°
12.
13. possible answers: concentric rings on cross
sections of trees (annual rings),bull’s-eye or target,
ripples from a rock falling into a pond.
14.
15.
P Q
65�
215�
16. Equilateral quadrilateral. (The figure is
actually a rhombus, but students have not yet
learned the properties needed to conclude that the
sides are parallel.)
17. equilateral; 3 to 1
18.
19. yes; yes
20. yes; no
21. no; no
y
x8 16
8
y
x
5
–5
–5
5
y
x
5
–5
–5
5
s
A
QP
B
18 ANSWERS TO EXERCISES
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22. 80°. The slices of pizza do not overlap, so
60° � x � 140°, where x is the measure in
degrees of the angle of the second slice.
23.
24. not possible
25.
26.
27. about 0.986°
28. 15°
29.
30.
T R
P A
F
T
A100�
C B
A
B
C A
31.
32. not possible
33.
34.
35.
36.
37. E
I
TK
120�
E2p
2p
2p 2p
I U
Q55�
50� 50�70� 70�
4a + 2b
T
R
G
120�120� 120�60�
120�60� 60�
60�
ANSWERS TO EXERCISES 19
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LESSON 1.8
1. 2.
3. 4.
5. 6.
7. 8.
9. 60 boxes 10.
11. 12.
13. B, D 14. B
15. C 16. D
17. A
18. 19.
20. true 21. true
5
3 4
2
34
22. False. The two lines are not necessarily in the
same plane, so they might be skew.
23. true 24. true
25. true
26. False. They divide space into seven or eight
parts.
27. true 28. (�3, 1)
29. perimeter � 20.5 cm; m(largest angle) � 100°
30.
120�
13 cm
8 cm
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LESSON 1.9
1. Sample answer: Furniture movers might
visualize how to rotate a couch to get it up a
narrow staircase.
2. yes
3. W O M E N����; Nadine is ahead.
4. 28 posts
5. 28 days
6. 0 ft (The poles must be touching!)
7.
8.
9.
10.
11. no
12. C�(�2, 3), A�(0, 0), B�(0, 5), D�(�2, 1)
13. Y�(�4, 1), C�(3, �1), N�(0, 3)
14. (x, y) → (x � 3, y � 2)
15. AB��� � CP���, EF��� � GH���; i � k, j � k
16. perimeter � 34 cm
17. Left photo: Three points determine a plane.
Middle photo: Two intersecting lines determine a
plane. Right photo: A line and a point not on the
line determine a plane.
Polygons
Quadrilaterals
Trapezoids
Triangles
Obtuse Isosceles
BA
BA
3 cm
3 cm
3 cm
A
A
B
A B
18. pyramid with hexagonal base
19. prism with hexagonal base
20. pyramid with square base
21. x � 15, y � 27
22. x � 12, y � 4
23.
24.
25. point, line, plane
26. AB��� 27. AB�
28. vertex 29. AB��30. AB��� � CD�� 31. protractor
32. �ABC 33. AB�� CD���
34. congruent to
35. The distance is two times the radius.
36. They bisect each other and are perpendicular.
QP
B
A
PQ = 2r
QP
rr
ANSWERS TO EXERCISES 21
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CHAPTER 1 REVIEW
1. true
2. False; it is written as QP��.
3. true
4. False; the vertex is point D.
5. true
6. true
7. False; its measure is less than 90°.
8. false; two possible counterexamples:
9. true
10. true
11. False; they are supplementary.
12. true
13. true
14. true
15. False; it has five diagonals.
16. true
17. F
18. G
19. L
20. J
21. C
22. I
23. no match
24. A
25. no match
26.
27.
28.
N
A
G
R
I E
S
PT
5
7
3
O
E Y
T
K
C
AA
CD
D
BPP
�APD and �APCare a linear pair.
�APD and �APCare the same angle.
29.
30.
31.
32.
33.
34.
35.
36.
37.
40�
125�
2 in.
3 in.5 in.
DC
A
B
T
A
P
R T
A P
EY
22 ANSWERS TO EXERCISES
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38. 114°
39. x � 2, y � 1
40. x � 12, y � 4
41. x � 4, y � 2.5
42. x � 10, y � 8
43. AB � 16 cm
44. 96°
45. 105°
46. 30°
47.
48. 66 inches
49. 3 feet
50. The path taken by the midpoint of the ladder is
an arc of a circle or a quarter-circle if the ladder
slides all the way from the vertical to the horizontal.
Shed
Path of flashlight
Quadrilateral
Rectangle Square Rhombus
Trapezoid
51. He will get home at 5:46 (assuming he goes
inside before he gets blown back again).
52. (2, 3)
53.
54.
55.
56.
57.