Download Document

Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
Pages 6–9 Exercises
1. 80, 160
12. 1 , 1
2. 33,333; 333,333
13. James, John
3. –3, 4
14. Elizabeth, Louisa
4.
1, 1
16 32
5 6
15. Andrew, Ulysses
5. 3, 0
16. Gemini, Cancer
6. 1, 1
17.
3
20. The sum of the first 30 pos.
even numbers is
30 • 31, or 930.
21. The sum of the first 100
pos. even numbers is
100 • 101, or 10,100.
7. N, T
8. J, J
19. The sum of the first 6 pos.
even numbers is
6 • 7, or 42.
18.
9. 720, 5040
10. 64, 128
11. 1 , 1
36 49
1-1
Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
22. The sum of the first
100 odd numbers is
1002, or 10,000.
28. 1 ÷ 1 = 3 and 3 is
2
3
2
2
improper.
29. 75°F
25–28. Answers may vary.
Samples are given.
25. 8 + (–5 = 3) and 3 >/ 8
26.
1 • 1 > 1 and 1 • 1 > 1
/
/ 2
3 2
3 2 3
27. –6 – (–4) < –6 and
–6 – (–4) < –4
32. 10, 13
33. 0.0001, 0.00001
23. 555,555,555
24. 123,454,321
31. 31, 43
30. 40 push-ups;
answers may vary.
Sample: Not very
confident, Dino may
reach a limit to the
number of push-ups
he can do in his
allotted time for
exercises.
1-1
34. 201, 202
35. 63, 127
36. 31 , 63
32 64
37. J, S
38. CA, CO
39. B, C
Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
40. Answers may vary.
Sample: In Exercise
31, each number
increases by increasing
multiples of 2. In Exercise
33, to get the next term,
divide by 10.
42.
43.
44.
41.
45.
You would get a third line
between and parallel to
the first two lines.
46. 102 cm
1-1
47. Answers may vary.
Samples are given.
a. Women may soon outrun
men in running competitions.
b. The conclusion was based
on continuing the trend
shown in past records.
c. The conclusions are
based on fairly recent
records for women,
and those rates of
improvement may not
continue. The conclusion
about the marathon is most
suspect because records
date only from 1955.
Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
48. a.
b. about 12,000 radio
stations in 2010
c. Answers may vary.
Sample: Confident;
the pattern has held
for several decades.
49. Answers may vary.
Sample: 1, 3, 9, 27,
81, . . .
1, 3, 5, 7, 9, . . .
50. His conjecture is
52.
probably false
because most
53.
people’s growth
slows by 18 until
they stop growing
somewhere between
18 and 22 years.
51. a.
b. H and I
c. a circle
1-1
21, 34, 55
a. Leap years are years
that are divisible by 4.
b. 2020, 2100, and 2400
c. Leap years are years
divisible by 4, except
the final year of a
century which must
be divisible by 400.
So, 2100 will not be a
leap year, but 2400
will be.
Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
54. Answers may vary.
Sample:
55. (continued)
d.
100 + 99 + 98 + … + 3 + 2 + 1
1 + 2 + 3 + … + 98 + 99 + 100
101 + 101 + 101 + … + 101 + 101 + 101
56. B
The sum of the first 100 numbers is
57. I
100 • 101 , or 5050.
2
The sum of the first n numbers is n(n+1) .
2
55. a. 1, 3, 6, 10, 15, 21
b. They are the same.
c. The diagram shows the product of n
and n + 1 divided by 2 when
n = 3. The result is 6.
1-1
58. [2] a. 25, 36, 49
b. n2
[1] one part correct
Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
59. [4] a. The product of 11
and a three-digit
number that begins
and ends in 1 is a
four-digit number
that begins and ends
in 1 and has middle
digits that are each
one greater than the
middle digit of the
three-digit number.
(151)(11) = 1661
(161)(11) = 1771
59. (continued)
[3] minor error in
explanation
60-67.
[2] incorrect description
in part (a)
[1] correct products for
(151)(11), (161)(11),
and (181)(11)
68. B
b. 1991
69. N
c. No; (191)(11) = 2101
70. G
1-1
Patterns and Inductive Reasoning
GEOMETRY LESSON 1-1
Find a pattern for each sequence.
Use the pattern to show the next
two terms or figures.
Use the table and inductive reasoning.
1. 3, –6, 18, –72, 360
–2160; 15,120
2.
3. Find the sum of the first 10 counting numbers.
55
4. Find the sum of the first 1000
counting numbers.
500,500
Show that the conjecture is false by finding one
counterexample.
5. The sum of two prime numbers is an
even number.
Sample: 2+3=5, and 5 is not even
1-1
Points, Lines, and Planes
GEOMETRY LESSON 1-2
Pages 13–16 Exercises
1. no
2. yes; line n
3. yes; line n
4. yes; line m
5. yes; line n
6. no
7. no
8. yes; line m
16. BCGH
9. Answers may vary.
Sample: AE, EC, GA
10. Answers may vary.
Sample: BF, CD, DF
17. RS
18. VW
19. UV
11. ABCD
20. XT
12. EFHG
21. planes QUX and QUV
13. ABHF
22. planes XTS and QTS
14. EDCG
23. planes UXT and WXT
15. EFAD
24. UVW and RVW
1-2
Points, Lines, and Planes
GEOMETRY LESSON 1-2
25.
27.
29.
30. S
26.
28.
31. X
32. R
33. Q
34. X
1-2
Points, Lines, and Planes
GEOMETRY LESSON 1-2
35. no
36. yes
37. no
38. coplanar
39. coplanar
40. noncoplanar
41. coplanar
42. noncoplanar
44. Answers may vary.
Sample: The plane of
the ceiling and the
plane of a wall
intersect in a line.
45. Through any three
noncollinear points
there is exactly one
plane. The ends of the
legs of the tripod
represent three
noncollinear points, so
they rest in one plane.
Therefore, the tripod
won’t wobble.
43. noncoplanar
1-2
46. Postulate 1-1: Through
any two points there is
exactly one line.
47. Answer may vary.
Sample:
48.
49. not possible
Points, Lines, and Planes
GEOMETRY LESSON 1-2
50.
56.
54.
51. not possible
52.
no
no
55.
57.
yes
no
53.
yes
58.
yes
yes
1-2
Points, Lines, and Planes
GEOMETRY LESSON 1-2
59.
65. never
yes
60. always
61. never
68. Answers may vary.
Sample:
66. a. 1
b. 1
c. 1
d. 1
e. A line and a point
not on the line are
always coplanar.
67.
Post. 1-3: If two planes
intersect, then they
intersect in exactly one
line.
62. always
69. A, B, and D
63. always
70. Post. 1-1: Through any
two points there is
64. sometimes
Post. 1-4: Through
three noncollinear
points there is exactly
one plane.
1-2
exactly one line.
Points, Lines, and Planes
GEOMETRY LESSON 1-2
71. Post. 1-3: If two planes
intersect, then they
intersect in exactly one
line.
72. The end of one leg
might not be coplanar
with the ends of the
other three legs. (Post.
1-4)
74.
76.
yes
no
75.
77.
73.
no
yes
yes
1-2
Points, Lines, and Planes
GEOMETRY LESSON 1-2
80.
78.
no
79. Infinitely many;
explanations may vary.
Sample: Infinitely many
planes can intersect in
one line.
By Post. 1-1, points D
and B determine a line
and points A and D
determine a line. The
distress signal is on
both lines and, by Post.
1-2, there can be only
one distress signal.
1-2
81. a. Since the plane is
flat, the line would
have to curve so as
to contain the 2
points and not lie in
the plane; but lines
are straight.
b. One plane; Points A,
B, and C are
noncollinear. By
Post. 1-4, they are
coplanar.
Then, by part (a),
AB and BC are
coplanar.
82. 1
Points, Lines, and Planes
GEOMETRY LESSON 1-2
83. 1
4
90.
91. I, K
84. 1
92. 42, 56
85. A
93. 1024, 4096
86. I
94. 25, –5
87. B
95. 34
88. H
96. 44
89. [2] a. ABD, ABC, ACD,
BCD
b. AD, BD, CD
[1] one part correct
The pattern 3, 9, 7, 1
repeats 11 times for n = 1
to 44. For n = 45, the last
digit is 3.
1-2
Points, Lines, and Planes
GEOMETRY LESSON 1-2
Use the diagram at right.
1. Name three collinear points.
D, J, and H
2. Name two different planes that contain points C and G.
planes BCGF and CGHD
3. Name the intersection of plane AED and plane HEG.
HE
4. How many planes contain the points A, F, and H?
1
5. Show that this conjecture is false by finding one counterexample:
Two planes always intersect in exactly one line.
Sample: Planes AEHD and BFGC never intersect.
1-2
Segments, Rays, Parallel Lines and Planes
GEOMETRY LESSON 1-3
Pages 19-23 Exercises
1.
2.
7. a. TS or TR, TW
b. SR, ST
12. BC
13. BE, CF
3.
8. 4; RY, SY, TY, WY
4.
9. Answers may vary.
Sample: 2; YS or YR,
YT or YW
15. AD, AB, AC
10. Answers may vary.
Check students’ work.
17. ABC || DEF
5. RS, RT, RW, ST,
SW, TW
6. RS, ST, TW, WT,
TS, SR
11. DF
1-3
14. DE, EF, BE
16. BC, EF
Segments, Rays, Parallel Lines and Planes
GEOMETRY LESSON 1-3
18-20 Answers may vary.
Samples are given
18. BE || AD
19. CF, DE
20. DEF, BC
21. FG
22. Answers may vary.
Sample: CD, AB
23. BG, DH, CL
25. true
31. False; they are ||.
26. False; they are skew.
32. False; they are ||.
27. true
33. Yes; both name the
segment with
endpoints X and Y.
28. False; they intersect
above CG.
29. true
34. No; the two rays have
different endpoints.
30. False; they intersect
above pt. A.
35. Yes; both are the line
through pts. X and Y.
24. AF
1-3
Segments, Rays, Parallel Lines and Planes
GEOMETRY LESSON 1-3
41. never
36.
42. sometimes
43. always
44. sometimes
37. always
38. never
39. always
40. always
49. a. Answers may vary.
Sample: northeast
and southwest
b. Answers may vary.
Sample: northwest
and southeast, east
and west
50. Two lines can be
parallel, skew, or
intersecting in one
46. sometimes
point. Sample: train
tracks–parallel; vapor
47. sometimes
trail of a northbound jet
and an eastbound jet
48. Answers may vary.
at different altitudes–
Sample: (0, 0); check
skew; streets that
students’ graphs.
cross–intersecting
45. always
1-3
Segments, Rays, Parallel Lines and Planes
GEOMETRY LESSON 1-3
51. Answers may vary.
55. a. The lines of
Sample: Skew lines
intersection are
cannot be contained in
parallel.
one plane. Therefore,
they have “escaped” a
b. Examples may vary.
plane.
Sample: The floor
and ceiling are
52. ST || UV
parallel. A wall
intersects both. The
lines of intersection
53. Answers may vary.
are parallel.
Sample: XY and ZW
intersect at R.
56. Answers may vary.
Sample: The diamond
structure makes it
tough, strong, hard,
and durable. The
graphite structure
makes it soft and
slippery.
57. a.
one segment; EF
b.
54. Planes ABC and DCBF
intersect in BC.
3 segments; EF,
EG, FG
1-3
Segments, Rays, Parallel Lines and Planes
GEOMETRY LESSON 1-3
58. No; two different
planes cannot intersect
in more than one line.
57. c.
59. yes; plane P, for
example
Answers may vary.
Sample: For each
“new” point, the
number of new
segments equals
the number of “old”
points.
d. 45 segments
61. QR
62. Yes; no; yes;
explanations may vary.
63. D
64. H
65. B
66. F
67. B
60. Answers may vary.
Sample: VR, QR, SR
e. n(n – 1)
68. C
69. D
2
1-3
Segments, Rays, Parallel Lines and Planes
GEOMETRY LESSON 1-3
71–78. Answers may vary.
70. [2] a. Alike: They do
Samples are given.
not intersect.
Different: Parallel
71. EF
lines are coplanar
and skew lines lie
72. A
in different
planes.
73. C
b. No; of the 8 other
lines shown, 4
intersect
JM and 4 are
skew to JM.
80.
81.
82. 1.4, 1.48
83. –22, –29
74. AEF and HEF
84. FG, GH
75. ABH
85. P, S
76. EHG
86. No; whenever you
subtract a negative
number, the answer is
greater than the given
number. Also, if you
subtract 0, the answer
stays the same.
77. FG
[1] one likeness, one
difference
79.
78. B
1-3
Segments, Rays, Parallel Lines and Planes
GEOMETRY LESSON 1-3
Use the figure below for Exercises 1-3.
Use the figure below for Exercises 4 and 5.
1. Name the segments that
4. Name a pair of parallel planes.
form the triangle.
RS, TR, ST
plane BCD || plane XWQ
2. Name the rays that have point T
5. Name a line that is skew to XW.
as their endpoint.
TO, TP, TR, TS
AC or BD
3. Explain how you can tell that
no lines in the figure are parallel or skew.
The three pairs of lines intersect,
so they cannot be parallel or skew.
1-3
Measuring Segments and Angles
GEOMETRY LESSON 1-4
Pages 29–33 Exercises
1. 9; 9; yes
9. 25
15. 130
2. 9; 6; no
10. a. 13
b. RS = 40, ST = 24
16.
XYZ,
ZYX, Y
17.
MCP,
1
PCM,
18.
ABC,
CBA
19.
CBD,
DBC
3. 11; 13; no
4. 7; 6; no
5. XY = ZW
6. ZX = WY
11. a. 7
b. RS = 60, ST = 36,
RT = 96
12. a. 9
b. 9; 18
7. YZ < XW
13. 33
8. 24
14. 34
1-4
C or
Measuring Segments and Angles
GEOMETRY LESSON 1-4
20-23. Drawings may vary.
20.
21.
24. 60; acute
33. –2.5, 2.5
25. 90; right
34. –3.5, 3.5
26. 135; obtuse
35. –6, –1, 1, 6
27. 34
36. a. 78 mi
b. Answers may vary.
Sample: measuring
with a ruler
28. 70
22.
29. Q
37–41. Check students’
work.
30. 6
23.
31. –4
32. 1
1-4
Measuring Segments and Angles
GEOMETRY LESSON 1-4
42. true; AB = 2, CD = 2
43. false; BD = 9, CD = 2
49. Answers may vary.
Sample: (15, 0), (–9, 0),
(3, 12), (3, –12)
44. false; AC = 9, BD = 9,
AD = 11, and 9 + 9 =/
11
50–54. Check students’ work.
45. true; AC = 9, CD = 2,
AD = 11, and 9 + 2 =
11
56–58. Answers may vary.
Samples are given.
55. about 42°
60. 150
61. 30
62. 100
63. 40
64. 80
65. 125
56. 3:00, 9:00
46. 2, 12
66. 125
57. 5:00, 7:00
47. 115
58. 6:00, 12:32
48. 65
59. 180
1-4
Measuring Segments and Angles
GEOMETRY LESSON 1-4
67–68. Answers may vary.
Samples are given.
67.
68.
69.
QVM and
MNP and
MQV and
VPN
71. y = 15; AC = 24,
DC = 12
72. ED = 10, DB = 10,
EB = 20
MVN
PNQ
70. a. 19.5
b. 43; 137
c. Answers may
vary. Sample: The
sum of the
measures should
be 180.
73. a. Answers may vary.
Sample: The two
rays come together
at a sharp point.
75. 12; m AOC = 82,
m AOB = 32,
m BOC = 50
76. 8; m AOB = 30,
m BOC = 50,
m COD = 30
77. 18; m AOB = 28,
m BOC = 52,
m AOD = 108
b. Answers may vary.
Sample: Molly had
an acute pain in her 78. 7; m AOB = 28,
m BOC = 49,
knee.
m AOD = 111
74. 45, 75, and 165, or
135, 105, and 15
1-4
79. 30
Measuring Segments and Angles
GEOMETRY LESSON 1-4
80. a–c. Check students’ 86. [2] a.
work.
87. never
81. Angle Add. Post.
89. always
82. C
83. F
84. D
85. H
88. never
b. An obtuse
measures between
90 and 180 degrees;
the least and greatest
whole number values
are 91 and 179
degrees. Part of ABC
is 12°. So the least and
greatest measures
for DBC are 79 and
167.
[1] one part correct
1-4
90. never
91. always
92. always
93. always
94. never
95. 25, 30
96. 3125; 15,625
97. 30, 34
Measuring Segments and Angles
GEOMETRY LESSON 1-4
Use the figure below for Exercises 1-3.
Use the figure below for Exercises 4–6.
1. If XT = 12 and XZ = 21, then TZ = 7.
9
2. If XZ = 3x, XT = x + 3, and TZ = 13,
find XZ.
24
3. Suppose that T is the midpoint of XZ.
If XT = 2x + 11 and XZ = 5x + 8,
find the value of x.
14
4. Name 2 two different ways.
DAB, BAD
5. Measure and classify 1, 2,
and BAC.
90°, right; 30°, acute; 120°, obtuse
6. Which postulate relates the measures
of 1, 2, and BAC?
Angle Addition Postulate
1-4
Basic Construction
GEOMETRY LESSON 1-5
Pages 37-40 Exercises
1.
9. a. 11; 30
b. 30
c. 60
6.
2.
10. 5; 50
3.
7.
11. 15; 48
12. 11; 56
4.
13.
5.
8.
1-5
Basic Construction
GEOMETRY LESSON 1-5
14.
16. Find a segment on XY
so that you can
construct YZ as its
bisector.
15.
1-5
17. Find a segment on SQ
so that you can
construct SP as its
bisector. Then bisect
PSQ.
Basic Construction
GEOMETRY LESSON 1-5
18. a. CBD; 41
b. 82
c. 49; 49
19. a-b.
20. Locate points A and B
on a line. Then
construct a at A and
B as in Exercise 16.
Construct AD and BC
so that AB = AD = BC.
21. (continued)
b. Infinitely many;
there’s only 1 midpt.
but there exist
infinitely many lines
through the midpt. A
segment has exactly
one bisecting line
because there can
be only one line
21. Explanations may vary.
to a segment at its
Samples are given.
midpt.
a. One midpt.; a midpt.
divides a segment into
c. There are an infinite
two segments. If
number of lines in
there were more than
space that are to a
one midpt. the
segment at its midpt.
segments wouldn’t be .
The lines are coplanar.
20. (continued)
1-5
Basic Construction
GEOMETRY LESSON 1-5
22.
23.
24.
25. They are both correct.
If you mult. each side
of Lani’s eq. by 2, the
result is Denyse’s eq.
26. Open the compass to
more than half the
measure of the
segment. Swing large
arcs from the endpts.
to intersect above and
below the segment.
Draw a line through the
two pts. where the arcs
intersect. The pt. where
the line and segment
intersect is the midpt.
of the segment.
1-5
27.
28. a.
They appear to
meet at one pt.
Basic Construction
GEOMETRY LESSON 1-5
28. (continued)
b.
30.
33. a.
c. The three
bisectors of a
intersect in one pt.
29.
31. impossible; the short
segments are not long
enough to form a .
32. impossible; the short
segments are not long
enough to form a .
1-5
b. They are all 60°.
c. Answers may vary.
Sample: Mark a pt.,
A. Swing a long arc
from A. From a pt. P
on the arc, swing
another arc the
same size that
intersects the arc at
a second pt., Q.
Draw PAQ. To
construct a 30° ,
bisect the 60° .
Basic Construction
GEOMETRY LESSON 1-5
34. a-c.
35, (continued)
c. Point O is the center
of the circle.
36.
; the line intersects.
37. D
38. F
35. a-b.
39. [2] a.Draw XY. With the
compass pt. on B
swing an arc that
intersects BA and BC.
Label the intersections
P and Q, respectively.
With the compass
point on X, swing a arc
intersecting XY.
1-5
39. [2] (continued)
Label the intersection K.
Open the compass to PQ.
With compass pt. on K,
swing an arc to intersect
the first arc. Label the
intersection R. Draw XR.
Basic Construction
GEOMETRY LESSON 1-5
41.
39. [2] b. With compass
40. (continued)
open to XK, put
42.
c. Draw AB. Do
compass point on X
constructions as in
43.
and swing an arc
parts a and b. Open 44.
intersecting XR. With
the compass to the
45.
compass on R and
length of the shortest
open to KR, swing an
segment in part b.
arc to intersect the first
With the pt. of the
arc. Label intersection
compass on B, swing
46.
T. Draw XT.
an arc in the opp.
47.
[1] one part correct
direction from A
intersecting AB at C. 48.
40. [4] a. Construct its
AC = 1.25 (AB).
bisector.
49.
b. Construct the bisector. [3] explanations are not
Then construct the
thorough
50.
bisector of two new
[2] two explanations correct
segments.
[1] part (a) correct
1-5
6
10
4
3
100
20 and 180
No; they do not have
the same endpt.
Yes; they both
represent a segment
with endpts. R and S.
Basic Construction
GEOMETRY LESSON 1-5
Use the figure at right.
NQ bisects DNB.
For problems 1-4, check students’ work.
1. Construct AC so that AC NB.
2. Construct the perpendicular bisector of AC.
3. Construct
RST so that
RST
4. Construct the bisector of
RST.
QNB.
5. Find x. 17
6. Find m
DNB. 88
1-5
The Coordinate Plane
GEOMETRY LESSON 1-6
Pages 46–49 Exercises
1. 6
11. about 4.5 mi
21. (6, 1)
2. 18
12. about 3.2 mi
22. (–2.25, 2.1)
3. 8
13. 6.4
23. (3 7 , –3)
4. 9
14. 15.8
24. (10, –20)
5. 23.3
15. 15.8
25. (5, –1)
6. 10
16. 5
26. (0, –34)
7. 25
17. B, C, D, E, F
27. (12, –24)
8. 12.2
18. (4, 2)
28. (9, –28)
9. 12.0
19. (3, 1)
29. (5.5, –13.5)
10. 9 mi
20. (3.5, 1)
30. (8, 18)
8
1-6
The Coordinate Plane
GEOMETRY LESSON 1-6
31. (4, –11)
40. 2.2; (3.5, 1)
32. 5.0; (4.5, 4)
41. IV
33. 5.8; (1.5, 0.5)
42.
43.
34. 7.1; (–1.5, 0.5)
ST =
(5 – 2)2 + (–3 – (–6))2 =
9 + 9 = 3 2 4.2
TV =
(6 – 5)2 + (–6 – (–3))2 =
1 + 9 = 10 3.2
35. 5.4; (–2.5, 3)
36. 10; (1, –4)
37. 2.8; (–4, –4)
38. 6.7; (–2.5, –2)
39. 5.4; (3, 0.5)
The midpts. Are the
same, (5, 4). The
diagonals bisect each
other.
VW =
(5 – 6)2 + (–9 – (–6))2 =
9 + 9 = 3 2 3.2
SW =
(5 – 2)2 + (–9 – (–6))2 =
9+9=3 2
4.2
No, but ST = SW and TV = VW.
1-6
The Coordinate Plane
GEOMETRY LESSON 1-6
44. 19.2 units; (–1.5, 0)
50. 1073 mi
45. 10.8 units; (3, –4)
51. 2693 mi
46. 5.4 units; (–1, 0.5)
52. 328 mi
47. Z; about 12 units
53–56. Answers may
vary. Samples are
48. 165 units; The dist. TV
given.
is less than the dist.
TU, so the airplane
53. (3, 6), (0, 4.5)
should fly from T to V
to U for the shortest
54. E (0, 0), (8, 4)
route.
55. (1, 0), (–1, 4)
49. 934 mi
56. (0, 10), (5, 0)
1-6
57. exactly one pt.,
E (–5, 2)
58. exactly one pt.,
J (2, –2)
59. a–f. Answers may
vary. Samples are
given.
a. BC = AD
b. If two opp. sides of a
quad. are both || and
, then the other
two opp. sides are
.
The Coordinate Plane
GEOMETRY LESSON 1-6
59. (continued)
c. The midpts. are the
same.
59. (continued)
f. If a pair of opp.
sides of a quad. are
both || and , then
d. If one pair of opp.
the segment joining
sides of a quad. are
the midpts. of the
both || and , then
other two sides has
its diagonals bisect
the same length as
each other.
each of the first pair
of sides.
e. EF = AB
60. A (0, 0, 0)
B (6, 0, 0)
C (6, –3.5, 0)
D (0, –3.5, 0)
E (0, 0, 9)
F (6, 0, 9)
G (0, –3.5, 9)
1-6
61.
62. 6.5 units
63. 11.7 units
64. B
65. I
The Coordinate Plane
GEOMETRY LESSON 1-6
66. A
70.
73.
71.
74. 10
67. C
68. A
69. [2] a. (–10, 8), (–1, 5),
(8, 2)
b. Yes, R must be
(–10, 8) so that
RQ = 160.
75. 10
76. 48
72.
77.
TAP,
78. 150
[1] part (a) correct or
plausible explanation
for part (b)
1-6
PAT
The Coordinate Plane
GEOMETRY LESSON 1-6
A has coordinates (3, 8). B has coordinates (0, –4). C has coordinates (–5, –6).
1. Find the distance between A and B to the nearest tenth. 12.4
2. Find BC to the nearest tenth. 5.4
3. Find the midpoint M of AC to the nearest tenth. (–1, 1)
4. B is the midpoint of AD. Find the coordinates of endpoint D. (–3, –16)
5. An airplane flies from Stanton to Mercury in a straight
flight path. Mercury is 300 miles east and 400 miles south
of Stanton. How many miles is the flight? 500 mi
6. Toni rides 2 miles north, then 5 miles west, and then 14 miles
south. At the end of her ride, how far is Toni from her starting
point, measured in a straight line? 13 mi
1-6
Perimeter, Circumference, and Area
GEOMETRY LESSON 1-7
Pages 55–58 Exercises
16.
1. 22 in.
9. 10
2. 36 cm
10. 3.7
3. 56 in.
11. 2
1
ft
in.
m
14.6 units
4. 78 cm
12. 56.5 in.
5. 120 m
13. 22.9 m
6. 48 in.
14. 1.6 yd
7. 38 ft
15. 351.9 cm
17.
8. 15 cm
25.1 units
1-7
Perimeter, Circumference, and Area
GEOMETRY LESSON 1-7
1
3
18.
20. 1 ft2 or 192 in.2
29. 9
21. 4320 in.2 or 3 yd2
30. 0.25
22. 1 1 ft2 of 162 in.2
31. 9.9225
23. 8000 cm2 or 0.8 m2
32. 0.01
64
in.2
m2
ft2
8
16 units
19.
24. 5.7
m2
or 57,000
25. 120,000
26. 6000
27. 400
ft2
cm2
cm2
or 12
m2
2
or 666 yd2
3
m2
m2
33. 153.9 ft2
34. 54.1 m2
35. 452.4 cm2
36. 452.4 in.2
37. 310 m2
38 units
28. 64
ft2
1-7
38. 19 yd2
Perimeter, Circumference, and Area
GEOMETRY LESSON 1-7
39. 24 cm2
40. 80 in.2
41. a. 144 in.2
b. 1 ft2
c. 144; a square
whose sides are 12
in. long and a
square whose sides
are 1 ft long are the
same size.
43. 3289 m2
44–47. Answers may
vary. Samples are
given.
44. 38 in.; 90 in.2
45. 39 in.; 93.5 in.2
48. Answers may vary.
Sample: For Exercise
46, you use feet
because the bulletin
board is too big for
inches. You do not use
yards because your
estimated lengths in
feet were not divisible
by 3.
46. 12 ft; 8 ft2
49. 16 cm
47. 8 ft; 3.75 ft2
50. 96 cm2
42. a. 30 squares
b. 16; 9; 4; 1
c. They are =.
Post 1-10
51. 288 cm
1-7
Perimeter, Circumference, and Area
GEOMETRY LESSON 1-7
52. a. Yes; every square is
a rectangle.
54.
56. 38 units
57. 54 units2
b. Answers may vary.
Sample: No, not all
rectangles are
squares.
c. A = (
P
4
2
)
or A =
P2
16
58. 1,620,000 m2
perimeter = 10 units
area = 4 units2
59. 30 m
60. (4x – 2) units
55.
61. Area; the wall is a
surface.
53. 512 tiles
perimeter = 16 units
area = 15 units2
1-7
62. Perimeter; weather
stripping must fit the
edges of the door.
Perimeter, Circumference, and Area
GEOMETRY LESSON 1-7
63. Perimeter; the fence
must fit the perimeter
of the garden.
64. Area; the floor is a
surface.
65. 6.25
units2
66. a. base
1
2
3
24
25
26
47
48
49
height
98
96
94
:
:
52
50
48
:
:
6
4
2
1-7
area
98
192
282
b.
1248
1250
1248
282
192
98
c. 25 ft by 50 ft
Perimeter, Circumference, and Area
GEOMETRY LESSON 1-7
67. a.
b.
c.
d.
9
9
9
9
3a
units2
20
2
69. 25a units2
4
68.
70. (9m2 – 24mn + 16n2)
units2
71. Answers may vary.
Sample: one 8 in.-by-8
in. square + one 5 in.by-5 in. square + two
4 in.-by-4 in. squares
72. 388.5 yd
73. 64
74. 2336
83. 9.2 units; (1, 6.5)
75. 540
84. 6.7 units; (–2.5, –2)
76. 216
85. 90
77. 810
86. WI
78. (15, 13)
87. 62 units
79. 8.5 units; (5.5, 5)
88. 18 units
80. 5.8 units; (1.5, 5.5)
89. 6 units
81. 13.9 units; (3, 5.5)
90. 33 units
82. 6.4 units; (–2, 3.5)
1-7
RI
Perimeter, Circumference, and Area
GEOMETRY LESSON 1-7
A rectangle is 9 ft long and 40 in. wide.
1. Find the perimeter in inches. 296 in.
2. Find the area in square feet.
30 ft2
3. The diameter of a circle is 18 cm. Find the area in
terms of
.
81
cm2
4. Find the perimeter of a triangle whose vertices
are X(–6, 2), Y(8, 2), and Z(3, 14). 42 units
5. Find the area of the figure below. All angles are right angles.
256 in.2
1-7
Tools of Geometry
GEOMETRY CHAPTER 1
Page 64
1. Div. each preceding
term by –2; 1 , – 1
2
4
2. Add 2 to the preceding
term; 10, 12
4. Answers may vary.
Sample:
1, 2, 4, 8, 16, 32, . . .
1, 2, 4, 7, 11, 16, . . .
In the first seq. double
each term. In the
second seq., add
consecutive counting
numbers.
3. Rotate the U clockwise
one-quarter turn.
5. A, B, C
Alphabet is backwards;
6. Answers may vary.
Sample: A, B, C, D
7. Answers may vary.
Sample: A, B, D, E
8. B
9. a.
b.
c.
d.
1
infinitely many
1
1
10. 29,054.0 ft2
11. never
12. sometimes
13. never
14. always
15. never
1-A
Tools of Geometry
GEOMETRY CHAPTER 1
16. 10
17. a. (11, 19)
b. MC = MD =
136
18. 19.1 units
24. Answers may vary.
Sample: Some ways of
naming an can help
identify a side or
vertex.
25.
19. 800 cm2 or 0.08 m2
20. 12.25 in.2
21. 63.62 cm2
22. 7
23. 9
26.
bisector
27. VW
28. 7 units
1-A
29. AY
30. E, AY
31. 33 1 yd2
3