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CHAPTER 1
Chapter Opener
10. Every other number is zero. The other numbers alternate
between 3 and 3. The next two numbers are 3 and 0.
Chapter Readiness Quiz (p. 2)
1. A
2. J
3. A
1.1 Practice and Applications (pp. 5–7)
4. J
11.
12.
13.
14.
15.
16.
Lesson 1.1
1.1 Checkpoint (pp. 3–4)
1. The number of equal sections in the circle increases
by one.
2. The shaded triangle in the figure moves over one triangle
counterclockwise.
3. Each number after the first is 4 more than the previous
number.
17. Each number is 5 greater than the previous number. The
next number is 19 5 24.
4. Each number after the first is 5 less than the previous
number.
18. Each number is 9 less than the previous number. The next
number is 25 9 34.
1
19. Each number is the previous number. The next number
4
5
is 5 4 .
4
20. Each number is 2 times the previous number. The next
number is 20 2 40.
5.
6.
21. Numbers after the first are found by adding consecutive
7. Each number after the first is 3 less than the previous
number. The next two numbers are 11 3 14 and
14 3 17.
whole numbers. So, the sixth number is 6 more than the
fifth number which is 15 6 21.
22. Numbers after the first are found by adding consecutive
8. Each number after the first is 6 more than the previous
number. The next two numbers are 22 6 28 and
28 6 34.
even integers. So, the sixth number is 10 more than the
fifth number which is 25 10 35.
23. Each x-coordinate is odd, and each y-coordinate is 3.
Another point in the pattern is (5, 3).
1.1 Guided Practice (p. 5)
1.
2.
24. Each x-coordinate is odd, and each y-coordinate equals
its respective x-coordinate. Another point in the pattern
is (5, 5).
25. For each point, the x-coordinate is even, and the y-coordi-
3.
nate is 2 less than half the opposite of the x-coordinate.
4.
5. Each number is 8 greater than the previous number. The
next two numbers are 27 8 35 and 35 8 43.
6. Each number is 3 times the previous number. The next
two numbers are 54 3 162 and 162 3 486.
7. Each number is 0.5 greater than the previous number. The
next two numbers are 8.5 0.5 9 and 9 0.5 9.5.
8. Each number is 6 less than the previous number. The next
two numbers are 5 6 11 and 11 6 17.
1
9. Each number is the previous number. The next two
4
1
numbers are 4 4 1 and 1 4 .
4
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All rights reserved.
1
Another point in the pattern is 2, (2) 2
2
or (2, 3).
26.
Figure
1
2
3
4
5
6
Distance
4
8
12
16
20
24
27. Each distance is 4 times the figure number.
28. The nth figure would have a distance of 4n units.
29. The tenth figure would have a distance of 4 10 40
units.
30. Yes, because 60 is divisible by 4. 60 4 15, so the
fifteenth figure has a distance of 60 units.
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
9
Chapter 1 continued
31.
F F F F F
F F F F F F
F C C C C C F
F C C C C C C F
F F F F F
F F F F F F
43. 1.04
44. 18.39
46–53.
45. 45.24
y
E
32. After 8 doubling periods, there will be 3 28768
billions of bacteria.
33. The pattern is that the second ten letters is the same as
A
F
the first ten letters except there is one more raised dot in
the bottom left corner in each letter.
G
I
P
R
B
1
1
T
x
D
H
G
34. The pattern is 1, 1 3 4, 4 5 9, . . . . The next
object will have 9 7 16 blocks.
C
35. The pattern is 1, 1 5 6, 6 9 15, . . . . The next
object will have 15 13 28 blocks.
1.1 Standardized Test Practice (p. 7)
36. C; 55, 55 55 110, 110 55 165, 165 55 220,
220 55 275
37. H; 1, 1 4 5, 5 8 13, 13 12 25,
25 16 41
1.1 Mixed Review (p. 7)
Lesson 1.2
1.2 Geo-Activity (p. 8)
1. 4 people can shake hands 6 ways.
2. 5 people can shake hands 10 ways.
3.
People
2
3
4
5
Handshakes
1
3
6
10
4. Numbers after the first are found by adding consecutive
38. 6 ways;
whole numbers. So, the number of ways that 6 people
can shake hands is 10 5 or 15 ways.
Robert–Susan–Todd
Robert–Todd–Susan
1.2 Checkpoint (pp. 9–10)
Susan–Robert–Todd
1. The product of any two odd numbers is an odd number.
Susan–Todd–Robert
Todd–Robert–Susan
2. The product of the numbers (n 1) and (n 1) is n2 1.
Todd–Susan–Robert
3. Sample answer: The product of 1 and 2 is a counter-
example. The product 1 2 2 is even, but 1 is odd.
39. Sample answer:
4. Sample answer:
3 ft
1 ft 3 ft 2
10
6
4 ft
2 ft
8
ft 2
10
5 ft
3 ft
These shapes have two sides the same length, but they are
not rectangles.
15 ft 2
6 ft
4 ft
6
1.2 Guided Practice (p. 11)
1. A conjecture is an unproven statement based on a pattern
24 ft 2
or observation.
7 ft
2. You can prove a conjecture is false by finding one
counterexample.
5 ft
35 ft 2
3. The difference of any two odd numbers is even.
4. The sum of an odd number and an even number is odd.
5. The number 6 is a counterexample. It is divisible by two
1.1 Algebra Skills (p. 7)
40. 9.5
10
41. 11.3
42. 16
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
(6 2 3) but it is not divisible by four.
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 1 continued
6. The difference of 1 and 3 is a counterexample. The
16. The pattern of days between these full moons is 29, 30,
difference is 1 (3) 2 which is greater than 1.
7. Sample answer: A circle cannot be drawn around any of
the four-sided shapes shown.
29, 30, 29, . . . . The next full moon will occur in 30
days, or Saturday, January 14.
17. The product of 2 and 4 is a counterexample because
(2)(4) 8, which is a positive number, but neither
factor is positive.
18.
1.2 Practice and Applications (pp. 11–13)
6 ft
4 ft
8 ft
A
2 ft
B
8.
These two rectangles each have a perimeter of 20 feet;
however, rectangle A has an area of 24 square feet and
rectangle B has an area of 16 square feet.
30
42
19.
12
9.
12
20
This triangle has two sides that are the same length, but
the third side is longer than either of those sides.
20. The pattern suggests that the next key would have the
15
letters P, Q, and R. However, the next key has P, Q, R,
and S or P, R, and S.
21
10. 101 25 2525
101 34 3434
21. x (x 1) (x 2) (x 3) (x 4)
(x x x x x) (1 2 3 4)
101 49 4949
5x 10
The product of 101 and any two digit number is the
number formed by writing the two digit number twice.
5(x 2)
The factors of the sum of five consecutive integers
beginning with x are 5 and (x 2). Because 5 is a
factor, the sum is divisible by 5.
11. 11 11 121
111 111 12,321
1111 1111 1,234,321
The square of an n-digit number of all ones is the number obtained by writing the consecutive digits from 1 to
n in increasing order, then the digits from n 1 to 1 in
decreasing order. This pattern does not continue beyond
n 9.
12. 3 4 12
1.2 Standardized Test Practice (p. 13)
22. B
23. H
1.2 Mixed Review (p. 13)
24.
25.
4
W
33 34 1122
333 334 111,222
The product of an n-digit number consisting of all threes
and an n-digit number consisting of the number 3 as
the first n 1 digits and the number 4 as the last digit is
the number obtained by writing 1 n-times followed by 2
n-times.
13. The product of an odd number and an even number is an
1.2 Algebra Skills (p. 13)
26. 5
27. 7
30. 15
28. 10
34. 10
35. 2
38. 15
39. 3
29. 10
32. 4
31. 14
36. 6
40. 27
33. 4
37. 11
41. 54
even number.
14. The sum of three consecutive integers is always three
times the middle number.
15. The number of diagonals after a 3-sided figure is found
by adding consecutive integers starting with two. So a
seven sided figure will have 9 5 14 diagonals and an
eight sided figure will have 14 6 20 diagonals.
Lesson 1.3
1.3 Checkpoint (pp. 15–16)
1. line n, line m, and line p
2. plane T and plane S
3. Points C, D, and E lie on the same line, so they
are collinear.
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All rights reserved.
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
11
Chapter 1 continued
4. Sample answer: Points A, D, and E do not lie on
the same line.
15. Sample answer: Points A, B, C, and D
5. Points B, C, D and E lie on the same plane, so they
are coplanar.
6. line n and line p, or line m and line p.
7.
A
1.3 Practice and Applications (pp. 17–20)
B
16. ^&(
BC and DE
^&(
17. plane S or plane ABC
18. plane T or plane ADE
C
19. false
23. true
D
8.
A
B
C
^&(
AB and ^&
AC( are the same lines because points A, B, and C
are collinear.
B
C
D
Line segments AC
**** and BD
**** are not the same because the
segments have different endpoints.
10.
A
24. true
21. true
22. true
25. false
27. K
28. N
29. M
31. L
32. F
33. J
26. true
30. F
34. M
35. Sample answer: N, P, and R
D
9. A
20. false
B
C
36. Sample answer: R, S, and T
37. Sample answer: W, A, and X
38. D
39. G
40. H
41. H
42. E
43. E
44. G
45. H
46. P, Q, R, and S
47. N, K, R, and Q
48. R, S, L, and K
49. M, N, P, and Q
50. K, L, M, and N
51. P, M, S, and L
52. Q, R, M, and L
53. S, R, M, and N
54. Sample answer: A, P, U, and E
D
55. Sample answer: A, Q, and B
CA
&*( and CB
&*( are the same rays because they have the
same endpoints and extend in the same direction.
1.3 Guided Practice (p. 17)
56. Sample answer: QR
**** , BR
**** , AC
****, and BD
****
57. ^&
BE(, RU
^&(, ^&(,
CF and ^&(
SP divide the board in half.
58. points K and N
59. Sample answer: K, N, and Q
^&(: line PQ
1. PQ
PQ
**** : segment PQ
60. plane JKL and plane JKN
PQ
&*( : ray PQ
61. plane KNM and plane QNM
QP
&*( : ray QP
62. Yes, because K, N, J, and Q lie on the same wall;
2. PQ
&*( has endpoint P and extends toward Q but QP
&
*( has
endpoint Q and extends toward P.
3. false
therefore, they lie on the same plane.
63.
J
4. true
K
5. True, although the plane is not shown.
6. false
9.
7. true
R
S
T
True
False
10.
R
11.
12.
S
L
8. false
M
64.
A
65.
B
C
H
T
R
S
T
R
S
T
False
F
66. yes
True
J
67. yes
G
68. no
69. no
1.3 Standardized Test Practice (p. 20)
70. D
13.
R
14.
12
S
R
False
T
S
1.3 Mixed Review (p. 20)
T
True
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
71. Each number is 11 more than the previous number.
The next number is 39 11 50.
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 1 continued
72. Each number is 5 less than the previous number.
The next number is 6 5 11.
2. ^&(
TV and QU
^&( intersect at point U.
3. ^&(
PS and UV
^&( do not appear to intersect.
73. Each number is 5 times the previous number.
4. Planes X and Y intersect at line p.
The next number is 500 5 2500.
74. Each number after the first is found by adding consecu-
tive multiples of 5. The next number is 50 25 75.
5. Planes Y and Z intersect at line q.
6. Planes Z and X do not appear to intersect.
7.
j P
1.3 Algebra Skills (p. 20)
75. 0.5
76. 0.75
k
77. 0.6
79. 0.6
w 0.67
80. 1.3
w 1.33
81. 0.7
w 0.78
82. 5.5
78. 0.4
8.
m
9.
n
R
S
W
Quiz 1 (p. 20)
1.
2.
1.4 Guided Practice (p. 25)
3. Sample answer: The number 30 is a counterexample,
because it is divisible by 10 (30 10 3) but it is not
divisible by 20.
1. The intersection of two or more figures is the point or
points that the figures have in common.
2. true
3. false
4. false
5. true
6. false
4. Sample answer:
This triangle has two sides
that are the same length.
4
3
4
7. The telephone poles illustrate the intersection of lines.
8. The arrow and target illustrate the intersection of a line
5. Sample answer: The sum of 0 and 1 is a counterexam-
ple, because 0 1 1 and 1 is not greater than 1.
6. Sample answer: If you fold the square in half along its
diagonal, then unfold it and cut along the fold, you will
create two triangles of the same size.
7. Sample answer:
8. Sample answer:
R
T
1.4 Practice and Applications (pp. 25–27)
P
V
Z
X
Y
Lesson 1.4
1.4 Activity (p. 21)
1. point G, point G
2. point G
3. ^&(
AB
4. CD
^&( and ^&(
EF are coplanar because CD
^&( intersects ^&(.
EF
5. point T
6. SW
^&(
7. The planes do not appear to meet.
1.4 Checkpoint (pp. 23–24)
1. ^&(
PS and QR
^&( intersect at point R.
Copyright © McDougal Littell Inc.
All rights reserved.
and a plane.
9. The screen panels illustrate the intersection of planes.
10. PQ
^&( and ^&(
TS intersect at point R.
11. ^&(
QS and ^&(
PT do not appear to intersect.
12. ^&(
SQ and ^&(
TR intersect at point S.
13. ^&
RS( and ^&(
PT intersect at point T.
14. ^RP
&( and ^&(
PT intersect at point P.
15. ^&
RS( and ^&(
ST are the same line so the intersection is ^&
RS(,
^&(,
ST or ^&(.
RT
16. Planes P and Q do not appear to intersect.
17. Planes Q and R intersect at line l.
18. Planes P and R intersect at line j.
19. Planes P and S intersect at line k.
20. Planes Q and S intersect at line m.
21. Planes R and S do not appear to intersect.
22. ^&(
AB and ^&(
BC intersect at point B.
23. ^&(
AD and ^&(
AE intersect at point A.
24. HG
^&( and DH
^&( intersect at point H.
25. Plane ABC and plane DCG intersect at DC
^&(.
26. Plane GHD and plane DHE intersect at DH
^&(.
27. Plane EAD and plane BCD intersect at ^&(.
AD
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
13
Chapter 1 continued
28. Sample answer:
40. Points A, B, and D are coplanar because three points
determine a plane. Point C is also in the plane because
it is on AD
&
*( , which is in the plane.
a
b
X
1.4 Algebra Skills (p. 27)
29. Sample answer:
t
M
s
41. 11.4
42. 6.2
43. 3.7
45. 8.57
46. 3.71
47. 7
50. 4
51. 2
52. 5
53. 2
44. 4.46
48. 3
49. 0
54. 5
r
30. Sample answer:
31. Sample answer:
Lesson 1.5
A
Y
B
Z
1.5 Checkpoint (pp. 28–30)
1
8
1
2
1. 2 inches
2. 1 inches
3. AC AB BC
C
14 6
32. Sample answer:
23 ST 15
20
5.
8 ST
y
C
A
k
j
4. SR ST TR
B
N
1
5 lines have 10 intersections
33.
1
D
x
AB ⏐3 (2)⏐ ⏐5⏐ 5
CD ⏐1 4⏐ ⏐5⏐ 5
Yes, there is a pattern. Each time a line is added to a
figure with n lines, n points of intersection are added.
AB
**** and CD
**** have the same length so AB
**** CD
**** .
6.
A y
1.4 Standardized Test Practice (p. 27)
34. a. Lines CA
^&( and DB
^&( intersect at vanishing point V. Lines
1
CE
^&( and DF
^&( intersect at vanishing point W.
C
D
b– d.
A
H
V
B
W
D
x
B
E
C
G
1
F
1.4 Mixed Review (p. 27)
35. Each x-coordinate is even and each y-coordinate is 3.
Another point in the pattern is (4, 3).
36. Each y-coordinate is one more than twice the x-coordinate.
Another point in the pattern is (2, 2(2) 1) or (2, 5).
37. Each y-coordinate is 2 times the x-coordinate. Another
point in the pattern is (2, 2(2)) or (2, 4).
38. Three collinear points are A, C, and D.
39. Sample answer: Three noncollinear points are A, B,
and D.
AB ⏐1 5⏐ ⏐6⏐ 6
CD ⏐1 5⏐ ⏐6⏐ 6
AB
**** and CD
**** have the same length so AB
**** CD
**** .
1.5 Guided Practice (p. 31)
1. Yes, the distance between M and N is the same as the
length of MN
****.
2. 28 mm
3. DF DE EF
4. PR PQ QR
49
35 24 QR
13
11 QR
5. AB ⏐4 1⏐ ⏐3⏐ 3
CD ⏐3 (1)⏐ ⏐4⏐ 4
EF ⏐1 3⏐ ⏐4⏐ ⏐4⏐ 4
So, CD
**** EF
**** because they have the same length.
14
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 1 continued
6. AB ⏐3 0⏐ 3
29.
y
R
CD ⏐3 3⏐ ⏐6⏐ 6
EF ⏐3 2⏐ ⏐5⏐ 5
GH ⏐4 1⏐ ⏐5⏐ 5
1
P
So, EF
**** GH
**** because they have the same length.
1
x
S
1.5 Practice and Applications (pp. 31–33)
7. 30 mm
8. 33 mm
10. 27 mm
13.
D
9. 25 mm
11. 18 mm
E
14.
F
DF DE EF
15.
N
M
PQ ⏐4 (2)⏐ ⏐6⏐ 6
12. 35 mm
G
RS ⏐1 5⏐ ⏐6⏐ 6
H
16.
P
NP NM MP
17. true
18. false
20. true
21. false
R
PQ
**** RS
**** because they have the same length.
J
GJ GH HJ
30.
y
S
1
QS QR RS
1
x
19. true
22. PR PQ QR
P
23. SU ST TU
97
5 16
16
21
24. LN LM MN
R
PQ ⏐3 (1)⏐ ⏐4⏐ 4
RS ⏐2 (3)⏐ ⏐5⏐ 5
25. JL JK KL
21 11 MN
10 MN
PQ
**** and RS
**** do not have the same length so they are not
congruent.
23 JK 17
6 JK
26. Difference Coral Grouper length Trout length
1
1
9 7
8
2
5
1 inches
8
Total length Coral Grouper length Trout length
1
1
9 7
8
2
5
16 inches
8
27. AB ⏐2 3⏐ ⏐5⏐ 5
CD ⏐3 (1)⏐ ⏐4⏐ 4
EF ⏐4 0⏐ ⏐4⏐ 4
31. AC AB BC
(x 2) (7x 3)
8x 1
PR PQ QR
32.
(13y 25) (8y 5) QR
(13y 25) (8y 5) QR
13y 25 8y 5 QR
5y 20 QR
LN LM MN
33.
(4z 15) (z 3) (z 4)
4z 15 2z 1
2z 16
GH ⏐2 (2)⏐ ⏐4⏐ 4
z8
So, CD
**** EF
**** GH
**** because they have the same length.
28. JK ⏐3 2⏐ ⏐5⏐ 5
LM ⏐4 (1)⏐ ⏐5⏐ 5
S
1.5 Standardized Test Practice (p. 33)
34. D
35. J
NP ⏐2 2⏐ ⏐4⏐ 4
QR ⏐3 (2)⏐ ⏐5⏐ 5
1.5 Mixed Review (p. 33)
So, JK
**** LM
**** QR
**** because they have the same length.
36. Sample answer: The number 6 is a counterexample
Copyright © McDougal Littell Inc.
All rights reserved.
because 6 is a multiple of 3 (3 2 6) but it is even.
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
15
Chapter 1 continued
5. ma ABC ma ABD ma DBC
37. Sample answer:
40 90
6
2.5
130
2.5
6. ma ABD ma ABC ma CBD
6
135 ma ABC 60
The perimeter of this rectangle is a counterexample
because 2(2.5) 2(6) 17.
38.
n
C
75 ma ABC
39.
q
E
D
1.6 Guided Practice (p. 38)
1. C
m
1.5 Algebra Skills (p. 33)
40. 3 6 2 3 12
15
41. 18 3 4 5 6 20
26
42. 7 11 3 8 7 33 8
43. 14 7 4 2 4
8
44. (8 5 6) 3 (3 6) 3
93
3
45. 2(7 5) 10 2(2) 10
4 10
14
Lesson 1.6
7. J, JH
&*(, JK
&
*(; about 75
8. S, SR
&*(, ST
&
*(; about 90
9. straight
10. acute
11. obtuse
14. Yes, a DEG a HEG because their measures are equal:
ma DEG ma DEF ma FEG 45 45 90 and
a GEH has a right angle mark which means that it is 90.
1.6 Practice and Applications (pp. 38–41)
15. X, XF
&*( , XT
&
*(
16. N, NK
&
*( , NE
&
*(
17. Q, QR
&*( , QS
&
*(
18. Any two of a A, a EAU, a UAE
19. Any two of a C, a BCD, a DCB
20. Any two of a T, a PTS, a STP
21. ma ABC 55
22. ma XYZ 25
23. ma DEF 140
24. acute; about 40
25. right; about 90
26. obtuse; about 150
27. ma ABC ma ABD ma DBC
45 60
105
28. ma DEF ma DEG ma GEF
60 120
180
1. a RST or a TSR or a S
29. ma PQS ma PQR ma RQS
a KMN or a NMK,
160 ma PQR 20
a HMN or a NMH
140 ma PQR
3. a GJF or a FJG,
a CJF or a FJC,
12. acute
13. Yes, a DEG a FEG because their measures are equal.
1.6 Checkpoint (pp. 35–37)
2. a HMK or a KMH,
4. A
6. M, ML
&
*( , MN
&*( ; about 120
1.6 Activity (p. 34)
1–4. Answers may vary.
3. B
5. E, ED
&*(, EF
&
*(; about 35
40 8
32
2. D
30.
y
C
a GJC or a CJG
4. ma ABC ma ABD ma DBC
60 20
80
16
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
1
B
1
A
x
a ABC is right.
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 1 continued
31.
32.
y
48. PM
&
* ( and PQ
&
*(
y
1
B
A
1
49.
x
1
A
B
1
a ABC is acute.
33.
51.
B
R
52.
C
J
K
L
JL JK KL
1.6 Algebra Skills (p. 41)
53.
A
x 3 15
y42
54.
x 3 3 15 3
C
1
y4424
x 12
1
x
55.
y 2
z79
34. about 74
35. about 82
36. about 88
37. about 117
38. about 158
39. 150
w 5 5 2 5
z 16
w3
57. 2p 24
58. 9 3q
2p
24
2
2
p 12
9
3q
3
3
3 q
59. 5r 125
60. 12 6s
40. ma 1 18(10) 15(10)
180 150
30
w 5 2
56.
z 7 7 9 7
a ABC is acute.
12
6s
6
6
2 s
5r
125
5
5
r 25
41. ma 2 18(10) 3(10)
180 30
150
42. ma 3 15(10) 3(10)
Quiz 2 (p. 41)
150 30
1. Sample answer: CB
^&( and DE
^&(
120
43.
A
P
PR PQ QR
AC AB BC
a ABC is obtuse.
y
B
50.
Z
XZ XY YZ
x
C
C
X Y
2. Sample answer: ^&(
BE and CB
^&( intersect at B.
ma 4 ma 3 180
3. Sample answer: DE
^&( and ^&(
BE intersect at E.
ma 4 120 180
4.
y
ma 4 60
C
44. The difference of the numbers on each end of a runway
is 18. So the runway opposite that of runway 3 would
be 3 18 21. Also,
1
A
ma 4 x(10) 15(10)
B x
1
D
60 10x 150
AB ⏐5 0⏐ ⏐5⏐ 5
210 10x
CD ⏐1 4⏐ ⏐5⏐ 5
21 x
AB
**** CD
**** because they have the same length.
1.6 Standardized Test Practice (p. 40)
5.
y
45. a. a AOB, a BOC, a COD, a DOE, a EOF, a FOG,
A
a GOH and a HOA
b. a AOC, a BOD, a COE, a DOF, a EOG, a FOH,
D
4
B
2
C
x
a GOA and a HOB
c. a AOD, a BOE, a COF, a DOG, a EOH, a FOA,
a GOB and a HOC
AB ⏐3 (3)⏐ ⏐6⏐ 6
CD ⏐6 6⏐ ⏐12⏐ 12
1.6 Mixed Review (p. 41)
46. Sample answer: PM
&
*(
Copyright © McDougal Littell Inc.
All rights reserved.
47. Sample answer: NQ
&
*(
AB
**** and CD
**** are not congruent because their lengths are
not equal.
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
17
Chapter 1 continued
6. right
7. obtuse
9. acute
8. straight
10. acute
18. The product of four consecutive numbers, plus 1,
is always a squared number.
11. acute
12. ma JKL ma JKM ma MKL
55 25
19. Sample answer: A counterexample is the number 1.
The cube of 1 is 1, but 1 is not greater than 1.
20. true
80
13. ma WXZ ma WXY ma YXZ
21. false
23.
L
N
22. false
K
105 ma WXY 30
75 ma WXY
M
14. ma TUW ma TUV ma VUW
95 35 ma VUW
60 ma VUW
J
24. TU
^&( and UV
^&( intersect at U.
25. Plane PQR and plane UVS intersect at ^&(.
QS
26. Plane RSV and plane QUV intersect at ^&(.
VS
Chapter 1 Summary and Review (pp. 42–45)
1. Coplanar lines are lines that lie in the same plane.
^&(.
27. Plane QSV and plane TUV intersect at UV
28. Sample answer:
29. Sample answer:
y
c
2. An angle consists of two rays that have the same
endpoint.
d
B
L
A
3. A conjecture is an unproven statement that is based
z
W
on a pattern or observation.
4. The endpoint of the rays that form an angle is called
30. AC AB BC
its vertex.
5. Two or more figures intersect if they have points in
common.
6. An angle that has a measure between 0 and 90 is
called an acute angle.
32.
7. Points on the same line are collinear points.
31. RT RS ST
10 37
50 RS 24
47
26 RS
y
P
1
8. An angle that has a measure of 180 is called a
1
x
straight angle.
9. Two angles that have the same measure are called
congruent angles.
R
10. A counterexample is an example that shows a conjecture
PQ ⏐5 3⏐ ⏐8⏐ 8
is false.
QR ⏐9 2⏐ ⏐7⏐ 7
11. An angle that has a measure between 90 and 180 is
called an obtuse angle.
PQ
**** and QR
**** are not congruent because their lengths are
not equal.
12. Two segments that have the same length are called
congruent segments.
33.
y
13. Each number is 9 greater than the previous number.
The next two numbers in the pattern are 32 9 41
and 41 9 50.
P
2
14. Each number is the previous number multiplied by 3.
The next two numbers in the pattern are 162 3 486
and 486 3 1458.
15. Each number is 10 less than the previous number.
The next two numbers in the pattern are 70 10 60
and 60 10 50.
16.
17.
2
x
R
PQ ⏐1 (5)⏐ ⏐6⏐ 6
QR ⏐2 4⏐ ⏐6⏐ 6
PQ
**** QR
**** because their lengths are equal.
34. ma ABC ≈ 35; acute
35. ma MNP 90; right
36. ma RST ≈ 140; obtuse
18
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.
Chapter 1 continued
37. ma DEF ma DEG ma GEF
15.
y
A
60 45
105
1
38. ma HJK ma HJL ma LJK
1
x
D
90 ma HJL 40
C
B
50 ma HJL
AB ⏐2 4⏐ ⏐6⏐ 6
39. ma MNP ma QNM ma QNP
CD ⏐1 5⏐ ⏐4⏐ 4
180 ma QNM 110
AB
**** and CD
**** are not congruent because their lengths
are not equal.
70 ma QNM
16. a FBE a EBD because they both have a measure
Chapter 1 Test (p. 46)
of 45:
ma FBD ma FBE ma EBD
1. Each number is 7 more than the previous number.
The next two numbers in the pattern are 24 7 31
and 31 7 38.
90 45 ma EBD
45 ma EBD;
2. Each number is 17 more than the previous number.
The next two numbers in the pattern are 5 17 22
and 22 17 39.
a FBE is labeled 45.
17. ma ABC ma DBC ma FBD ma ABF
180 50 90 ma ABF
3. Numbers after the first are found by adding consecutive
multiples of 4. So, the next two numbers in the pattern
are 25 16 41 and 41 20 61.
4. Each number is 0.6 greater than the previous number.
The next two numbers in the pattern are 4.6 0.6 5.2
and 5.2 0.6 5.8.
180 140 ma ABF
40 ma ABF
18. ma CBF ma CBD ma DBF
50 90
140
5. The product of any two even numbers is even.
6.
Figure
1
2
3
4
5
Distance (units)
8
10 12 14 16
7. Each distance is 2 greater than the distance around the
previous figure. The figure at stage 10 has a distance of
26 units.
19. ma EBA ma ABF ma FBE
40 45
85
20. Sample answer:
acute angle: a FBE, obtuse angle: a FBC,
straight angle: a ABC, right angle: a FBD
8. Sample answer: Q, T, N
21. ma ABC ma ABD ma DBC
9. Sample answer: S, T, U, P
10. point N
11. LQ
^&(
25 35
12. PR PQ QR
13. AC AB BC
60
11 6
26 AB 18
17
ma ABE ma ABC ma CBE
8 AB
14.
180 60 ma CBE
120 ma CBE
y
A
C
D
Chapter 1 Standardized Test (p. 47)
1
2
x
B
AB ⏐2 3⏐ ⏐5⏐ 5
1. C
Copyright © McDougal Littell Inc.
All rights reserved.
3. C
4. H
b. Sample answer:
acute angle: a JBD, obtuse angle: a FDG,
CD ⏐3 (2)⏐ ⏐5⏐ 5
AB
**** CD
**** because their lengths are equal.
2. H
5. a. A, B, D, F
straight angle: a ABD, right angle: a CBA
6. D
7. G
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
19
Chapter 1 continued
Chapter 1 Algebra Review (p. 49)
1. 3(2) 4(7) 6 28 34
2. 2(2) 2(7) 4 14 18
3. 6(2) 7 12 7 19
4. 5(2) 7(7) 10 49 59
5. 14(2) 4(7) 28 28 0
6. 7 2(2) 7 4 3
7. 5(2) 3(7) 10 21 11
8. 11(7) 4(2) 77 8 69
9. 3(7) 2(3) 21 (6) 15
10. 2 4(3) 2 (12) 14
11. 2 7 (3) 9 3 6
12. 2(2) 5(3) 4 (15) 19
13. 3x 2 13
3x 15
x5
n
14. 2 4
8
n
2
8
n 16
15. 4 5w 24
16. 6p 1 17
5w 20
6p 18
w4
y
17. 10 7
3
y
3
3
y 9
p3
18. 4z 11 15
4z 4
z1
9 2t 5
19.
14 2t
7 t
b
20. 1 6
4
b
7 4
28 b
20
Geometry, Concepts and Skills
Chapter 1 Worked-Out Solution Key
Copyright © McDougal Littell Inc.
All rights reserved.