my cheat cheat to geometry

Chapter 7 Answers Practice 7-1 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 7-2 1. " 51 5. 2 " 21 9. 35 " 114 13. 19 m 17. right

2. 4 " 7 3. 2 " 65 4. " 7 6. 18 " 2 7. 210 in.2 8. 24 " 10 cm2 2 ft 10. 46 in.

11. 78 ft 12. 279 cm 14. acute 15. right 16. obtuse 18. obtuse 19. acute

Practice 7-3

1. x = 2; y = " 3 3.

6.

2. a = 4.5; b = 4.5" 3

3 25"3 c = 50" 4. 8 " 2 5.

3 ;d = 3 28"3 7. 2 8. x = 15; y = 15 " 3 3

10. 42 cm 14. w b=3

11. 5.9 in.

10"3 = 3 ;x =

12. 10.4 ft, 12 ft

5; y = 5 " 2 ; z

5 "3 = 3

14 " 2

9. 3 " 2

13. 170 in.2

Practice 7-4

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Reteaching 7-1 1. Samples: 4

4 6

4 6

6

2. Samples: 3 6

2

3 8

3. 20 cm2 4. 55 in.2 8. Samples:

8

5. 6 m

6. 8 ft

7. 4 in.

4

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

3

6 8

9. 5 in.

10. 23 cm

11. 9 ft

Reteaching 7-2 1.–2. 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. 49 p m

Geometry Chapter 7

3 7 1. 8.7% 2. 10.9% 3. 15.3% 4. 10 5. 10 1 2 1 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 %

12

1. x = 7; y = 3.5 " 3 2. a = 60; c 3. p = 4 " 3; q = 8; x = 30 4. m 1 = 45; m 2 = 45; m 3 = 90; m 4 = 90 5. m 5 = 60; m 6 = 30; m 7 = 120 6. m 8 = 60; m 9 = 30; m 10 = 60 7. 12 " 3 8. 36.75 " 3 9. 75 " 3 10. 120 in.2 2 2 11. 137 in.

12. 97 in.

4. 49 5. 14 p 6 p - 21.2 p 8. 16 - 81 9. 4p 15 13. 2 p 14. 6p 18. 3 19. 2

Practice 7-8

4

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 7-6

2. 21.2 3. 49 6p p p 1 1 or 4 6. 8 7. 16 p or 16 10. 18 11. 89 p 12. 23 p 5p 63 25 15. 8 p 16. 3 p 17. p2 20. 10 1. 49p

15. a = 4;

16. p = 4 " 3; q = 4 " 3; r = 8; s = 4 " 6

Practice 7-5

Practice 7-7

3. Sample: 9, 16, and 25

4. They are equal.

5. The sum of the squares of the two legs equals the square of the 6. 4 " 5 7. 7 " 2 8. 8 9. 6 hypotenuse.

Answers

39

Chapter 7 Answers

(continued) 2. Sample: 135° 3. Sample: 2 cm 4. Sample: 3p 2 cm 5. Sample: 4.5 cm 6. They are approximately 4.7 cm 7. 5p 8. 10p 9. 5p 10. 20p 11. 5p equal.

3 3 2 6 15p 12. 25p 13.

2 6

Reteaching 7-3 1.–2. Sample:

Reteaching 7-7 1.–2. Sample: 3. Sample: 3.5 and 7 4. Sample: 3.5 and 7 5. Sample: They are approximately equal.

6. Check students’ work.

7. d = 2 " 3; e = 4 3 8"3 8. f = 4" ; g = 9. x = 3 " 3; y = 3 3 3 10. u = 6 " 3; v = 12

Reteaching 7-4

4 cm

3. Sample: 50 cm2

4. Sample: 50.3 cm2 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. Sample:

Reteaching 7-8 2. Sample: bases = 6 cm and 10 cm, height = 6 cm 3. Sample: 48 cm2 4. Check students’ work.

5. Sample:

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%

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

Reteaching 7-5 1.–2. Sample: radius apothem

3. Sample: apothem = 2.5, radius = 3.5, side = 5 4. yes 5. They are approximately equal.

6. 100 in.2 2 2 2 7. 200 ft 8. 72 cm 9. 8 m

Reteaching 7-6 1. 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. m SPQ = 180 - (m APS + m PSA) = 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 triangles are equal.

13. a2 + 2ab + b2 = 4(12 ab) + c2 or a2 + 2ab + b2 = 2ab + c2 14. By subtracting 2ab from both sides, you obtain a2 + b2 = c2 (The Pythagorean Theorem).

Enrichment 7-2 Friar Tuck is the winner. By using the Pythagorean Theorem, Friar Tuck’s string length is 4 " 2 + 2 " 5 or 10.1 in. Little John’s string length is 4 " 5 + 2 " 2 or 11.8 in.

Enrichment 7-3 1. " 2

40

Answers

2. " 3

3. " 4 or 2

4. "5

Geometry Chapter 7

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Enrichment 7-1

Chapter 7 Answers 3

1

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

1 1

9

or

3

1

10

11

2

1

1

8

Activity 2: Creating

1 1

Check students’ work.

14 15

7

1

Activity 1: Modeling

2

1 4 or 5

2 6

13

1

Chapter Project

1

1

5.

(continued)

Activity 3: Researching Check students’ work.

1

✔ Checkpoint Quiz 1

1

1

1. 37.2 m2 2. 20 ft2 3. 9.6 m 5. " 52 7.2 6. 7 " 2 9.9

Enrichment 7-4 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 = 12 h(b1 +

b2) = 12 hb2 .

side where b1 = 0. Hence A 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

2. 47 square units

3. 73 square

Enrichment 7-6 1.–5. © Pearson Education, Inc. All rights reserved.

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

4.

5.

Radius (r)

Diameter Circumference (d) (C)

1.15 cm 238 in.

4 in.

2.3 cm 4 34 in.

8 in.

7.222 cm 14.92 in.

8p

6. They are approximately equal.

8.

C d

3.14 3.14 p 3.14 3.14

Check student’s work.

Check student’s work.

7. p 3.14

Enrichment 7-8 1. 0.06 or

1 18

2. 0.41

Geometry Chapter 7

3.

0.63 or "3 1 1 "3

4. 200 ft2 8. 20.9 ft

1. 225 in.2 2. 240 m2 3. 15.6 ft2 4. 41.6 cm2 2 5. 192 ft 6. 21 square units 7. 120 square units 8. 50 square units 9. right 10. acute 11. obtuse 12. 2 " 41 13. 3 14. 7 " 2 ; 7 " 2 15. 4; 4" 3 16. Sample: Draw an altitude to form a 30°-60°-90° triangle.

The altitude is 4" 3, and the area is 32 " 3.

17. 13.5 cm 18. 20 square units 19. 12p 20. 36p 21. 45 p 22. 54 p 23. p5 24. 4.44 square units 25. 21.5% 26. 9.1%

Chapter 7 Test, Form B 1. 144 in.2 2. 480 m2 3. 27.7 ft2 4. 93.5 cm2 2 5. 108 ft 6. 36.4 square units 7. 336 square units 8. 35 square units 9. right 10. obtuse 11. acute 12. 2 " 85 13. 8 14. 4" 3; 8 " 3 15. 4" 2; 8 16. Sample: Because one angle of the

rhombus measures 120°, the adjacent angle measures 60°.

Draw an altitude forming a 30°-60°-90° triangle. The altitude 17. 11.8 ft 18. 28 is 6 " 3, and the area is 72 " 3.

2 19. 16p 20. 64p 21. 5 p 22. 25 p square units 6 23. p 24. 2.26 square units 25. 36.3% 26. 19.6%

Enrichment 7-7

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

1. 63 m2 2. 96 in.2 3. 47.8 cm2 2 2 5. 648 m 6. 96.4 in.

7. 6.9 in.

9. 12p in.2 10. 108p m2

Chapter 7 Test, Form A

Enrichment 7-5 1. 19.5 square units units

✔ Checkpoint Quiz 2

4. 61 in.

7. 114.5 m2

5. 21 11. 2

Alternative Assessment, Form C TASK 1: Scoring Guide Sample:

a.

b h

h

4. 0.21 b

Answers

41

Chapter 7 Answers

(continued)

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 h

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

b2

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.

TASK 2: Scoring Guide 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.

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

TASK 3: Scoring Guide

Q

Sample:

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

1

"2

1

( ( )

X

8 cm

()

triangle, so AB = , or "33.

"3

5 cm P

Answers

20. 16p - 24 " 3

21. 61.5 m2

22. Euclid

1

The perimeter is 6(2AB) =

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

5 cm

2 cm

)

1

42

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:

Y

b. PAB forms a 30°-60°-90°

The area is

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

18. Sample:

,

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

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

12"33 = 4 " 3.

1. B 8. C 14. D

2 " 3.

A

B

Geometry Chapter 7

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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.