geometry rbc a answers - mr....

Answers

Copyright © Big Ideas Learning, LLC Geometry All rights reserved. Answers

A1

Chapter 1 1.1 Start Thinking

When the vertex of the triangle is moved in any direction, its angle measure also changes. Because all three sides of the triangle are connected, this also affects the other angles; If one angle becomes lesser, the sum of the other angles must become greater, and vice versa. All angles must be in relation to one another so that the sum of their angles always equals the same amount ( )180 .°

1.1 Warm Up

1. triangle 2. pentagon 3. hexagon

4. octagon 5. rhombus 6. decagon

1.1 Cumulative Review Warm Up

1. 64b = 2. 26a = 3. 104c =

4. 5p = 5. 92c = 6. 44u =

1.1 Practice A

1. Sample answer: C, E

2. Sample answer: , AB CD

3. plane G 4. line s

5. Sample answer: N, T, W

6. Sample answer: M, N, V

7. V

8.

9. Sample answer: 10.

11. Sample answer: L 12. EF

13. M 14. Sample answer: A

15. point, line

1.1 Practice B

1. Sample answer: A, B, D

2. , AB EF

3. D, E, F 4. plane C

5. Sample answer: , EG EF

6. C, E 7. E

8. Sample answer: C

9. 10.

11.

12. plane; Because three points determine a plane, the three feet of a tripod create a plane on the ground.

13.

ray

14.

segment

15. infinite; zero

1.1 Enrichment and Extension

1. Sample answer: plane PMR, plane PQO, plane PON

2. PO 3. , , ST SR SN

4. no; yes 5. VW

6. plane TXW and plane VWX

7. plane ZVT, plane ZYT, plane ZVW

8. yes; The only place where all planes will meet in the pyramid is at point T.

A

c

H

G

M

X

C D

A

C

B M

N

a

c

b

−1 0 1 2 3 4 5

−2 −1 0 2 41 3−4 −3

Answers

Geometry Copyright © Big Ideas Learning, LLC Answers All rights reserved. A2

9. yes; When substituted into each equation, it is a solution.

10. no; It is not a solution to either equation.

1.1 Puzzle Time

I’LL MEET YOU HALFWAY IN THE MIDDLE FOR A SPLIT

1.2 Start Thinking

Set the compass to be more than half the length of the line segment. Draw a semicircle with the compass. Turn the compass around and do the same from the other side, so that the semicircles intersect above and below the line. Use the straightedge to connect the two intersections. The point where the new line intersects the original line is the midpoint of the original line.

1.2 Warm Up

1–8.


1. 3118 2. 3

41 3. 4

4. 14 5. 4

5 6. 357

1.2 Practice A

1. 14

1 in. 2. 58

2 in.

3. 4.

no yes

5.

yes

6. 8 7. 21 8. 17

9. The ruler is lined up at the 2-inch mark; 2 5.25 3.25AB = − =

10. 32 in.

11. true; F is on EG

between E and G.

12. true; C is on BD

between B and D.

13. false; A, B, and F are not collinear.

1.2 Practice B

1. 78

in. 2. 18

2 in.

3. 4.

yes no

5. 18 6. 12 7. 12.1

8. about 1020 mi

9. 2 25 32; 7; 27; 12;x x x AB BC+ = + = = = 39AC =

10. 13 4 74; 6; 53; 21;x x AB BC− = = = = 74AC =

11. 51.8 mi; the third day


1. a. 25 b. 45 c. 50 d. 70 e. 7 f. 95

2. a. 2 b. 3 c. 9 d. 7 e. 9 f. 5

3. or DG IL 4. BD 5. BF

6. 2 2 7 49 1752 4 4

9 56; ; ; x x x x LM MN+ + = = = =

7. 2 1 13; 16; 4; 9x x x LM MN+ + = = = =

8. 1 2 14 1 13 ; ; 2;

2 3 3 2x LM

x x+ + = + = − =

8

3LN =

1.2 Puzzle Time

HE WAS A GOOD RULER

x

y8

4

−8

−4

84−4−8

A

BC

D

E

FG

H

x

y2

−4

−2

42−2

U

V

S

Tx

y2

−4

−2

42−2

U V

S

T

x

y

2

−4

−2

42−2UV

S

T

x

y4

−8

−4

4−4−8

AB

C

Dx

y4

−4

84A

B

C D

Answers


A3

1.3 Start Thinking

Plot the two points. Draw a right triangle containing those points as vertices, along with a third point. Using the coordinate plane, calculate the side lengths of the legs 5 and 1. Then use the Pythagorean Theorem to find the length of the hypotenuse,

2 25 1 26 5.1.+ = ≈ This is the distance in blocks between the points.

1.3 Warm Up

1. 2 2. 12 3. 2− 4. 2


1. 62x = 2. 140x = 3. 69x = 4. 109x =

1.3 Practice A

1. line d; 30 2. ; 11ML

3. ; 28MR

4. M; 26

5.

6.

7. ( )3, 2 8. ( )4, 2 9. ( )2, 7

10. ( )7, 7− − 11. 5 12. about 6.3

13. about 5.6 cm; about 2.8 cm; The center of the square is the segment bisector of the diagonal.

14. 60 ft

1.3 Practice B

1. ; 38MW

2. line ; 30

3.

4. ( )2, 7 5. ( )0, 3 6. ( )3, 0

7. ( )5, 13 8. about 3.2 9. 5

10. no; If one side of the square is s, then the length of

the diagonal is 2 2 22 2.s s s s+ = =

11. yes; Sample answer: A segment can be bisected by two different lines.

12. about 2 mi; about 10.5 mi


1. 1 2 1 2 1 2 1 2

1 2 1 2

3 3, , , ,

4 4 2 2

3 3,

4 4

x x y y x x y y

x x y y

+ + + +

+ +

2. a. ( ) ( ) ( )7 132 23, , 2, 5 , 1, − − −

b. ( ) ( ) ( )7112 2, 5 , 1, 6 , , 7− −

3. 13; b− 4. ( ) ( )12, 3 and 4, 3− − −

5. yes; The distance between each vertex is 5.

6. ( )2, 1, 6 7. ( )5 52 2, 6,− − 8. ( )7 9 3

2 2 2, ,

9. 6 10. 107 11. 89

1.3 Puzzle Time

IT WANTED TO BE REDUCED

1.4 Start Thinking

quad-, penta-, hexa-; Sample answer: A quadraphonic sound is a form of surround sound involving four speakers. A pentathlon is an athletic competition for individuals consisting of five events. A hexapod is an animal having six feet, typically with three distinct sets of two legs.

1.4 Warm Up

1. 236 cm, 60 cmP A= =

2. 2274 in., 4386 in.P A= =

3. 225.24 in., 39.8161 in.P A= =

4. 224 in., 28 in.P A= =


1. 66 cm 2. 104 m

X YM

A

B

M

E FMNot drawn to scale

Answers


1.4 Practice A

1. quadrilateral; convex 2. hexagon; concave

3. about 16.5 units 4. 21 square units

5. 28 square units 6. about 22.6 units


9. 12 square units 10. 44 square units

11. ( )1, 3 ; 14 square units−

12. a. 360 ft b. 240 ft c. $1000

1.4 Practice B

1. heptagon; convex 2. decagon; concave

3. about 22.2 units 4. 7.5 square units

5. 28 square units 6. about 13.2 units


9. 36 square units 10. 48 square units

11. a. 265 ft b. 40 ft c. $242.50

12. 4 mi


1. 24 square units 2. 4 or 8x x= − =

3. a. about 0.063 square units

b. about 32 squares

c. about 2 square units

4. about 1 square unit

1.4 Puzzle Time

TOO MANY PROBLEMS

1.5 Start Thinking

If the angle is larger than a right angle, it is obtuse. If the angle is smaller than a right angle, it is acute.

1.5 Warm Up

1. 70x = ° 2. 179r = ° 3. 144n = °

4. 90y = ° 5. 65t = ° 6. 120w = °


1. 40r = ° 2. 25w = ° 3. 40y = ° 4. 45v = °

1.5 Practice A

1. , , XYZ ZYX Y∠ ∠ ∠

2. , , PQR RQS SQP∠ ∠ ∠

3. 110 ; obtuse° 4. , BEH CFI∠ ∠

5. , , , , AGD EBH BHE FCI CIF∠ ∠ ∠ ∠ ∠

6. 92° 7. 44° 8. 55° 9. 33x =

10. a. Sample answer: EFG∠ is acute, DFE∠ is right, FBC∠ is obtuse, ABC∠ is straight.

b. 15 angles

c. 70°

d. 110°

1.5 Practice B

1. 50 ; acute° 2. 90 ; right°

3. 130 ; obtuse° 4. 180 ; straight°

5. 44° 6. 46° 7. 47° 8. 23°

9. yes; Because an acute angle is less than 90 ,° the

sum of three acute angles can be equal to 180 .°

10. a. Sample answer: ACE∠ is acute, AEC∠ is right, CDE∠ is straight.

b. DAE∠

c. 58°

d. 119°


1. 6 51x< <

2. 40 , 24m DEG m FEG∠ = ° ∠ = °

3. 6; 24° 4. 2 3

5. 100° 6. 5, 12x y= =

7.

AD C

FE

B

130°

Answers


A5

8. 45° 9. 45° 10. 175°

11. 95° 12. 140° 13. 140°

1.5 Puzzle Time

IS A CARRIER

1.6 Start Thinking

The angle formed is now greater than 180 .° So, add the angle formed from the negative x-axis to its position in Quadrant III to 180° to get the total angle measure.

1.6 Warm Up

1. 3x = 2. 1c = − 3. 1x = −

4. 2n = 5. 15x = − 6. 4x = −


1. 14 8, 22n n− = =

2. ( )2 5 6 18, 3n n− = =

3. ( )14 7 2 , 4n n= − =

4. ( ) ( ) ( )2 6 2 4 5, 1,x x x x x+ = + + + + + =

2 3, 4 5, 6 7x x x+ = + = + =

1.6 Practice A

1. , FJG GJH∠ ∠ 2. , CAD EJF∠ ∠

3. , BAC EJG∠ ∠

4. 54° 5. 105°

6. 149 , 31m WXY m YXZ∠ = ° ∠ = °

7. 48 , 42m ABC m CBD∠ = ° ∠ = °

8. 4 and 5∠ ∠

9. yes; The sides form two pairs of opposite rays.

10. no; The sides do not form two pairs of opposite rays.

11. ( )24 180; 78 and 102x x+ + = ° °

12. 3 90; 22.5 and 67.5x x+ = ° °

13. ( )12 15 180; 50 and 130x x+ − = ° °

14. a. Sample answer: 1, 2∠ ∠

b. Sample answer: 2, 5∠ ∠

c. 6 and 5, 8 and 5∠ ∠ ∠ ∠

d. 60 ; 1 and 3° ∠ ∠ are vertical angles so they have the same angle measure.

1.6 Practice B

1. and AEB BEC∠ ∠ 2. and BEC HFJ∠ ∠

3. and CED HFK∠ ∠

4. 19° 5. 153.3°

6. 84 , 96m ABC m CBD∠ = ° ∠ = °

7. 23 , 67m WXY m YXZ∠ = ° ∠ = °

8. 1 and 2, 3 and 2∠ ∠ ∠ ∠

9. 7 and 8∠ ∠

10. yes; The sides form two pairs of opposite rays.

11. no; The sides do not form two pairs of opposite rays.

12. ( )2 9 90; 27 and 63x x+ + = ° °

13 4 180; 36 and 144x x+ = ° °

14. ( )12 51 180; 86 and 94x x+ + = ° °

15. never; The sum of the angle measures of a linear pair is 180 .°

16. sometimes; When the sides of two angles form two pairs of opposite rays that meet at a 90° angle, the sum of the angle measures is 180 .°


1. supplementary 2. complementary

3. neither 4. supplementary

5. neither 6. complementary

7. complementary: not possible, supplementary: 15π


9. complementary: 1134 ,π supplementary: 14

17π


5π

Answers



42π


1.6 Puzzle Time

BECAUSE THE TEACHER SAID IT WAS A PIECE OF CAKE

Cumulative Review

1. 1 2. 6 3. 2 4. 16

5. 6 6. 25 7. 4 8. 3

9. 13 10. 27 11. 25 12. 17

13. 3 14. 4 15. 12 16. 22

17. 2 18. 2 19. 4 20. 1−

21. 1 22. 6− 23. 6 24. 6−

25. 3 26. 4− 27. 3 28. 1

29. 9 30. 7− 31. 4 32. 8

33. 7 34. 4 35. 4 36. 5

37. 7 38. 8 39. 4 40. 6

41. 4 42. 3 43. 8 44. 3

45. 5 46. 6 47. 11x =

48. 45x = − 49. 32x = − 50. 39x = −

51. 16x = 52. 103x = 53. 16x =

54. 32x = − 55. 5x = 56. 8x = −

57. 8x = − 58. 11x = 59. 30x =

60. 282x = − 61. 64x = 62. 104x = −

63. 2perimeter 24 cm, area 24 cm= =

64. 2perimeter 20 mi, area 16 mi= =

65. 2perimeter 24 in., area 36 in.= =

66. 2perimeter 26 yd, area 42.25 yd= =

67. 2perimeter 30 mm, area 37.5 mm= =

68. 2perimeter 18 ft, area 19.25 ft= =

69. 2perimeter 27 km, area 30.375 km= =

70. 2perimeter 55.2 cm, area 126.96 cm= =

71. 2perimeter 30.4 in., area 57.76 in.= =

72. 52 in. 73. 22976 in.

74. 21008 ft 75. 2160 ft

76. 8a ≥

77. 1b > −

78. 19c < −

79. 14d ≤ −

80. 27f >

81. 35g ≤

82. 8h ≥ −

83. 4j <

84. 12k <

85. 6m < −

1086420

0−2

−1

−4−6 2 4 6

0−5

−19

−10−15−20−25−30

−4 0−8−12

−14

−16−20

2520 301510

27

50

40 8 12 16 20 24 28

35

32 36 40

0−2−4−6−8−10

1086420

16 2012840

0−2−4−6−8−10

Answers


A7

86. 4n ≥ −

87. 9p ≥

88. 21s ≥ −

89. 22t ≥ −

90. 52u >

91. 60v >

92. 13x = − 93. 3x = − 94. 13x = −

95. 6x = 96. 9x = 97. 6x = −

98. 8x = − 99. 2x = 100. 3x = −

101. 60x = − 102. 36x = − 103. 16x = −

104. 13x = − 105. 13x = 106. 3x =

107. 2x = − 108. 1x = 109. 7x =

110. 1x = − 111. 9x = 112. 1x =

113. 8x = 114. 48x = 115. 7x =

116.

AB CD≅

117.

AB ≅ CD

118.

AB ≅ CD

119.

AB CD≅

120. 45 121. 49 122. 7

123. 12 124. ( )32, 7M 125. ( )3 1

2 2, M −

126. ( )3, 7H 127. ( )3, 1H −

128. 58 129. 272 or 4 17

130. 17 131. 170

132. 13 133. 232 or 2 58

134. 514 135. 117 or 3 13

136. 202 137. 29

138. 50 , 40m ABD m DBC∠ = ° ∠ = °

139. 82 , 98m LMP m PMN∠ = ° ∠ = °

0−2−4−6−8−10

108

9

6420

−4 0−8−12−16−20−24−28

−21

−32

−4 0−8−12−16−20−24

−22

1008060

52

40200

100806040200

x

y

−4

−2

4−2−4

2

4A B

C

D

x

y

−4

−2

42−2−4

2

4A B

C

D

x

y

−2

42−4

2

4

A

BC D

x

y

42−4 −2

2

4

A BC

D

−4

geometry rbc a answers - mr....

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