Chapter 7 Answers

Chapter 10 Answers Practice 10-1 1. 8 2. 8 3. 60 4. 240 5. 2.635 6. 1.92 7. 0.8125 8. 9 9. 1500 10. 8.75 11. 3.44 12. 7 13. 110 14. 30 15. 16 16. 119 17. 12 18. 48 19. 40 20. 56

Practice 10-2

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1. 48 cm2 2. 784 in.2 3. 11.4 ft2 4. 90 m2 2 2 2 5. 2400 in. 6. 374 ft 7. 160 cm 8. 176.25 in.2 2 9. 54 ft 10. 42.5 square units 11. 96 " 3 square units 12. 36 " 3 square units 13. 45 cm2 14. 226.2 in.2 2 15. 49,500 m

Practice 10-3

8"3 8"3 = 3 ;d = 3

1. x = 7; y = 3.5 " 3 2. a = 60; c 3. p = 4 " 3; q = 8; x = 30 4. m1 = 45; m2 = 45; m3 = 90; m4 = 90 5. m5 = 60; m6 = 30; m7 = 120 6. m8 = 60; m9 = 30; m10 = 60 7. 12 " 3 8. 36.75 " 3 9. 75 " 3 10. 120 in.2 2 2 11. 137 in. 12. 97 in.

1. 4 : 5; 16 : 25 2. 5 : 3; 25 : 9 3. 3 : 4; 9 : 16 2 5. 9 : 5 6. 1 : 6 7. 8 : 3 8. 576 9. 5 in. 1152 2 10. 25 in. 11. 2 : 3 12. 1 : 2 13. 2 : 5 14. 108 ft2

4. 1 : 2 2700 7

cm2

17.

p 2

18. 3

Practice 10-8 7 3 1. 8.7% 2. 10.9% 3. 15.3% 4. 10 5. 10 1 1 2 6. 5 7. 10 8. 1 9. 5 10. 22.2% 11. 4.0% 12. 37.5% 13. 20% 14. 50% 15. 40% 16. 33 13 %

Reteaching 10-1 1. Samples: 4

4 6

4 6

6

2. Samples: 4

3 6

cm2

3. 20 4. 55 8. Samples:

Practice 10-4

© Pearson Education, Inc., publishing as Pearson Prentice Hall.

15. 63 16. 25 8p 3p 19. 2 20. 10

3 8

in.2

2

8

5. 6 m

6. 8 ft

7. 4 in.

4 12

3

6 8

9. 5 in.

Practice 10-5

10. 23 cm

11. 9 ft

1. 174.8 cm2 2. 578 ft2 3. 1250.5 mm2 2 2 4. 192.6 m 5. 1131.4 in. 6. 419.2 cm2 7. 324.9 in.2 8. 162 cm2 9. 37.6 m2 10. 30.1 mi2 11. 55.4 km2 12. 357.6 in.2 13. 9.7 mm2 14. 384.0 in.2 15. 54.5 cm2 16. 9.1 ft2 2 2 17. 80.9 m 18. 83.1 m 19. 65.0 ft2 20. 119.3 ft2 2 2 21. 8 m 22. 55.4 ft

Reteaching 10-2

Practice 10-6

2. Sample: bases = 6 cm and 10 cm, height = 6 cm 3. Sample: 48 cm2 4. Check students’ work. 5. Sample:

1 1

1. 32p 2. 16p 3. 7.8p 4. Samples: DFA , ABF 00 1 1 5. Samples: FE , FD 6. Samples: FEB , EDA 0 0 7. Samples: FE , ED 8. ACB 9. FCD 10. 32 11. 43 12. 54 13. 39 14. 71 15. 90 16. 50 17. 220 18. 140 19. 220 20. 130 21. 6p in. 22. 16p cm 23. 94 p m

Practice 10-7 1. 49p

2. 21.2 or 6. 18 7. 9 18 10. 5 p 11. 8 p p 4

3. 49 6p p 1 16 p or 16 12. 23 p

Geometry Chapter 10

4. 49 6p p 8. 16 - 81 13. 15 2p

21.2

5.

9. 4p 14. 6p

1 4p

1. Sample:

6. Sample: diagonals = 4 cm and 9 cm 8. Check students’ work. 9. 144 ft2 2 2 11. 75 m 12. 98.4 cm

7. Sample: 18 cm2 10. 112 in.2

Answers

39

(continued)

Reteaching 10-3

Enrichment 10-1

1.–2. Sample:

1. c; each segment is the hypotenuse of a right triangle with 2. No; the angles must be shown to be legs a and b. 3. They are congruent; SSS 4. 180 right angles. 5. 90; acute angles of a right triangle are complementary. 6. CPCTC 7. mSPQ = 180 - (mAPS + mPSA) = 180 - 90 = 90 8. Repeat steps similar to those in Exercises 4–7 to show that PQR, QRS, and RSP are 9. a + b; (a + b)2 = a2 + 2ab + b2 right angles. 2 10. c; c 11. a, b; 21 ab 12. The areas of congruent 13. a2 + 2ab + b2 = 4(12 ab) + c2 triangles are equal. or a2 + 2ab + b2 = 2ab + c2 14. By subtracting 2ab from both sides, you obtain a2 + b2 = c2 (The Pythagorean Theorem).

radius apothem

3. Sample: apothem = 2.5, radius = 3.5, side = 5 4. yes 5. They are approximately equal. 6. 100 in.2 7. 200 ft2 8. 72 cm2 9. 8 m2

Reteaching 10-4 1. 4 : 3; 16 : 9 2. 8 : 5; 64 : 25 4. 4 : 3 5. 4 : 5 6. 3 : 5 9. 9 : 25

3. 9 : 5; 81 : 25 7. 16 : 9 8. 16 : 25

Enrichment 10-2

Reteaching 10-5 1. 19.3 in.2 5. 363.3 in.2

2. 123.1 cm2 6. 126.3 in.2

3. 86.6 in.2 7a. 81 in.2

4. 172.0 in.2 7b. area of

square = s2

Reteaching 10-6 1. Sample:

1. Choose an interior point X; construct PX 6 BC, XQ 6 AC , and XR 6 AB. 2. A triangle is a trapezoid with one

side where b1 = 0. Hence A = 12 h(b1 + b2) = 12 hb2 . 3. Area of BDE = Area ABEC - Area ABDC = [ 21 h(y + x + b)] - [ 21 h(y + x )] = 12 hy + 21 hx + 12 hb - (12 hy + 21 hx) = 12 hb


Chapter 10 Answers

Enrichment 10-3

2. Sample: 135° 3. Sample: 2 cm 4. Sample: 3p 2 cm 5. Sample: 4.5 cm 6. They are approximately 4.7 cm 10p 7. 5p 8. 9. 5p 10. 20p 11. 5p equal. 3 3 2 6 15p 25p 12. 6 13. 2

2. 47 square units

3. 73 square

Enrichment 10-4 1. 14

2. 21

3. 43

4. 19

Enrichment 10-5

1. 36 cm2 2. 4 "3 cm or about 6.93 cm 4. A = 6 sin u, 0° u 180°

Reteaching 10-7 1.–2. Sample:

3. 6 cm

Enrichment 10-6 4 cm

1.–5. Object

cm2

cm2

3. Sample: 50 4. Sample: 50.3 5. They are approximately equal. 6. Check students’ work. 7. 25p ft2 8. 4p in.2 9. 64p m2 10. 20.25p ft2 2 2 11. 324p cm 12. 64p in. 13. 14 cm 14. 615 cm2

1. Quarter 2. CD 3. Circle with a radius of 4 in. 4. 5.

Radius (r) 1.15 cm 238 in. 4 in.

Diameter Circumference (d) (C) 2.3 cm 4 34 in. 8 in.

7.222 cm 14.92 in. 8p

Check student’s work. Check student’s work.

6. They are approximately equal. 8.

C d

3.14 3.14 p 3.14 3.14

7. p 3.14

Reteaching 10-8 1. Check students’ work. 2. 21% 3. Check students’ work. 4. Sample: They are approximately equal. 5. Sample: The ratio would tend to be close to 21%. 6. 43%

40

Answers

Geometry Chapter 10


1. 19.5 square units units

Chapter 10 Answers

(continued)

Enrichment 10-7

3 3 1. p 2. " 3 3. 3" 4. p - 3" 4 4 6. p4 7. 4 8. 1 9. p 10. " 2 12. p - 2

Enrichment 10-8 1. 0.06 or

1 18

2. 0.41

3.

Alternative Assessment, Form C 5. 21 11. 2

0.63 or "3 1 1 "3

b h

36 in.2; 30.25 in.2; the seams in the finished quilt block account for the difference.

b

A parallelogram with base b and height h has the same area as two triangles with base b and height h. Thus, the area of the parallelogram is: A = 2 (12 bh) = bh.

b.

b1

Activity 2: Creating

h

Check students’ work.

b2

Activity 3: Researching Check students’ work.

✔ Checkpoint Quiz 1 1. 37.2 m2 5. 200 ft2

2. 20 ft2 6. 648 m2

h

4. 0.21

Activity 1: Modeling


Sample:

a.

Chapter Project

3. 63 m2 4. 96 in.2 7. 37; 949

✔ Checkpoint Quiz 2


TASK 1: Scoring Guide

1. 119.3 ft2 2. 293.9 m2 3. 523.1 in.2 4. 6.9 in. 2 5. 20.9 ft 6. 10p mi; 25p mi 7. 18p cm; 81p cm2 p or about 21% 8. 4 2 9. 12 or 50% 4

A trapezoid with bases b1 and b2 and height h has the same area as two triangles. The bases of the two triangles are b1 and b2, and the heights of both are h. Thus, the area of the trapezoid is: A = 12 b1h + 21 b2h = 12 h(b1 + b2). 3 Student gives accurate explanations accompanied by clear and correct diagrams. 2 Student gives generally correct explanations, although there may be some errors in either the explanations or the diagrams. 1 Student gives inaccurate or incomplete explanations and diagrams. 0 Student makes little or no attempt.

Chapter 10 Test, Form A


1. 15.6 ft2 2. 41.6 cm2 3. 192 ft2 4. 80 square 5. 120 square units 6. 50 square units units 7. 64 8. 91 9. D 10. 18.8 cm2 11. 19.1 in.2 9 12. 268.4 ft2 13. 166.3 in.2 14. 172.0 cm2 15. Sample: Draw an altitude to form a 30°-60°-90° triangle. 16. 13.5 cm The altitude is 4" 3, and the area is 32 " 3. 17. 20 square units 18. 12p 19. 36p 20. 45 p 21. 54 p 22. p5 23. 4.44 square units 24. 21.5% 25. 9.1%

Sample: C(2, 8), D(-2, 5). The slopes of AB and CD are equal, and the slopes of BC and AD are equal, so ABCD is a parallelogram. The slopes of AB and BC are opposite reciprocals, so AB # BC, and ABCD is a rectangle. AB = 5 and BC = 5, so the area of ABCD is 25 square units.

Chapter 10 Test, Form B


1. 110.9 ft2 2. 649.5 cm2 ; 649.6 cm2 ; or 649.7 cm2 3. 40.2 ft2 4. 60 ft2 5. 92 cm2 6. 72 in.2 16 1 2 7. 81 8. 4 9. A 10. 72.7 in. 11. 42.2 cm2 12. 21.6 cm 13. 385 cm2 ; 386 cm2 ; or 387 cm2 14. 36p 15. 324p 16. 4p 17. 18p 18. 75.4 cm2 19. 144p cm2 20. 4p in.2

Geometry Chapter 10

3 Student gives correct answers and provides complete and accurate reasoning. 2 Student gives generally correct answers and reasoning. 1 Student gives generally incorrect answers and reasoning. 0 Student makes little or no attempt. Q

Sample: 1

a. QXY is a 45°-45°-90° triangle, so the apothem QY = XY = 1 , or "22.

"2

X

Y

The perimeter is 4(2XY) = 4(2"22) = 4 " 2 .

The area is (2XY)2 = 4 ? ("22)2 = 4 (24) = 2.

Answers

41

Chapter 10 Answers

(continued)

b. PAB forms a 30°-60°-90°

triangle, so AB = 1 , or "33.

P

"3

1

The perimeter is 6(2AB) = 12"33 = 4 " 3. The area is

A

1 1 2 ap = 2 (1)(4"3) =

B

2 " 3.


3 Student gives clear and correct diagrams and explanations. 2 Student gives diagrams and explanations that may contain some minor errors. 1 Student gives diagrams or explanations that contain major errors or omissions. 0 Student makes little or no effort.

TASK 4: Scoring Guide Sample: a. a circle b. a and r are nearly equal; p and C are nearly equal. c. If the number of sides is great enough that the polygon becomes indistinguishable from a circle, the two formulas are equivalent, and one can be derived from the other. For example: A = 21 ap A = 12 rC A = 12 r(2pr)

(r a and p C) (C = 2pr)

= pr2


3 Student gives correct answers to parts a and b and gives an adequate explanation relating the two formulas in part c. 2 Student gives correct answers to parts a and b but exhibits difficulty with the logic of part c. 1 Student gives answers and an explanation that may contain significant errors. 0 Student makes little or no effort.

Cumulative Review 1. B 8. H 14. J

2. G 3. D 4. J 5. C 6. J 7. C 9. A 10. G 11. B 12. J 13. A 15. A 16. J 17. Sample: You may have used the branches to climb into the tree. 18. Sample:

Suppose that an equilateral triangle has an obtuse angle. Then one angle in the triangle has measure greater than 90. This contradicts the fact that, in an equilateral triangle, the measure of each angle is 60. 19. Sample: 8 cm

5 cm

2 cm 5 cm

20. 16p - 24 " 3

42

21. 61.5

Answers

m2

22. Euclid

Geometry Chapter 10