CHAPTER 8

CHAPTER 8

Chapter Opener

Chapter Readiness Quiz (p. 410)

1. A; a rhombus has four congruent sides. 2. H

Lesson 8.1

8.1 Checkpoint (p. 412)

1. Convex; the polygon is not regular because it is equilateral but not equiangular.

2. Concave; the polygon is not regular because it is equilateral but not equiangular.

3. Convex; the polygon is regular because it is both equilateral and equiangular.

8.1 Guided Practice (p. 413)

1. Sample answer:

2. All the sides of an equilateral polygon are congruent, while all the angles of an equiangular polygon are congruent.

3. A regular polygon is both equilateral and equiangular. 4. convex 5. concave 6. convex 7. C 8. A 9. B

8.1 Practice and Applications (pp. 413?415)

10. convex 11. concave 12. concave 13. equiangular 14. equilateral 15. neither 16. Not regular; the polygon is equilateral but not equiangular. 17. Regular; the polygon is both equilateral and equiangular. 18. Not regular; the polygon is equilateral but not equiangular. 19. Regular; the polygon is both equilateral and equiangular. 20. Regular; the polygon is both equilateral and equiangular. 21. Not regular; the polygon is equiangular but not equilateral. 22. concave 23. concave 24. convex 25. Polygon C is convex; polygons A and B are concave. 26. No. Sample answer: None of the polygons appear to be

both equilateral and equiangular. 27. Yes. The sum of the measures of the angles of a

triangle is 180. So, the missing angle measure is 180 60 60 60. All three angles are congruent, so the triangle is equiangular.

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28. Yes. Opposite sides of a parallelogram are congruent, so all four sides are congruent and the parallelogram is equilateral.

29. Yes. Sample answer: 30. Yes. Sample answer:

31. Yes. Sample answer: 32. Yes. Sample answer:

33. 3 in. 5 15 in. 35. 4 ft 12 48 ft 36. 2x 120

x 60 38. 5x 5 60

5x 65 x 13

34. 7 cm 8 56 cm

37. x 9 15 x6

8.1 Standardized Test Practice (p. 415)

39. A 40. H

8.1 Mixed Review (p. 415)

41. Yes; the figure has five sides so it is a pentagon. 42. Yes; the figure has four sides so it is a quadrilateral. 43. Yes; the figure has eight sides so it is an octagon.

8.1 Algebra Skills (p. 415)

44. 52 5 5 25 46. 63 6 6 6 216

48. 36 62 6 50. 169 132 13

45. (4)2 (4) (4) 16 47. 25 2 2 2 2 2 32

49. 1 12 1

51. 5 2.2

Lesson 8.2

8.2 Activity (p. 416)

Step 3.

Polygon

Triangle Quadrilateral Pentagon Hexagon

Number of Number of Sum of measures sides triangles of interior angles

3

1

1 180 180

4

2

2 180 360

5

3

3 180 540

6

4

4 180 720

Geometry, Concepts and Skills

Chapter 8 Worked-Out Solution Key

119

Chapter 8 continued

1. 5 180 900; 6 180 1080 2. (n 2) 180

8.2 Checkpoint (pp. 418?420)

1. (n 2) 180 (5 2) 180 3 180 540; 111 118 130 109 ma G 540 468 ma G 540 ma G 72

2. (n 2) 180 (4 2) 180 2 180 360; 58 133 103 ma G 360 294 ma G 360 ma G 66

3. (n 2) 180 (7 2) 180 5 180 900; 140 140 90 130 150 120 ma G 900 770 ma G 900 ma G 130

4. (n 2) 180 (12 2) 180 10 180 1800; 1800 150 12

5. 73 90 60 x 46 360 x 269 360 x 91

6. 89 3x 116 92 360 3x 297 360 3x 63 x 21

7. x x 110 360 2x 110 360 2x 250 x 125

8. 70 3x 75 65 2x 360 5x 210 360 5x 150 x 30

8.2 Guided Practice (p. 420)

1. Any one of : a A, a B, a BCD, a D, a DEA; any one of: a FEA, a DCH, a BCG

2. (n 2) 180 3. (n 2) 180 (9 2) 180 7 180 1260 4. ma 1 65 40 180 5. ma 1 66 130 100 360 6. ma 1 115 86 89 360 7. ma 1 117 57 59 85 360

8.2 Practice and Applications (pp. 421?423)

8. (n 2) 180 (6 2) 180 4 180 720 9. (n 2) 180 (8 2) 180 6 180 1080 10. (n 2) 180 (4 2) 180 2 180 360 11. (n 2) 180 (10 2) 180 8 180 1440 12. (n 2) 180 (15 2) 180 13 180 2340 13. (n 2) 180 (20 2) 180 18 180 3240 14. (n 2) 180 (30 2) 180 28 180 5040 15. (n 2) 180 (52 2) 180 50 180 9000 16. (n 2) 180 (100 2) 180 98 180 17,640 17. (n 2) 180 (4 2) 180 2 180 360;

ma A 92 68 101 360 ma A 261 360 ma A 99

18. (n 2) 180 (6 2) 180 4 180 720; ma A 110 149 91 135 100 720 ma A 585 720 ma A 135

19. (n 2) 180 (5 2) 180 3 180 540; ma A 90 130 80 113 540 ma A 413 540 ma A 127

20. (n 2) 180 (6 2) 180 4 180 720; ma A 102 146 120 124 158 720 ma A 650 720 ma A 70

21. (n 2) 180 (6 2) 180 4 180 720; 720 120 6

22. (n 2) 180 (7 2) 180 5 180 900; 900 128.6 7

23. (n 2) 180 (3 2) 180 1 180 180; 180 60 3

24. 75 44 65 x 76 54 360 x 314 360 x 46

25. 2x 71 85 44 3x 360 5x 200 360 5x 160 x 32

26. No; it is not equilateral or equiangular. 27. (n 2) 180 (5 2) 180 3 180 540

120

Geometry, Concepts and Skills

Chapter 8 Worked-Out Solution Key

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Chapter 8 continued

28. 90 90 x 90 x 540

270 2x 540

2x 270

x 135

ma C ma E 135

29. (n 2) 180 (5 2) 180 3 180 540; 540 108 5

30. Answers will vary.

31. The sum of the measures of the exterior angles of a convex polygon is always 360.

32. The sum of the measures of the interior angles of a convex octagon is never 1440;

(n 2) 180 (8 2) 180 6 180 1080

33. The measures of the exterior angles of a convex polygon are sometimes equal.

34. (n 2) 180 (6 2) 180 4 180 720;

720 120; 120 60;

6

2

ma 1 ma 2 60

35. 360 60 n 360 60n

36. 360 20 n 360 20n

6n

18 n

37. 360 72 n 360 72n

38. 360 10 n 360 10n

5n

36 n

8.2 Standardized Test Practice (p. 423)

39. B; (n 2) 180 (6 2) 180 4 180 720 x 134 120 102 2x 130 720 3x 486 720 3x 234 x 78

40. H; ma P 2x 2(78) 156

8.2 Mixed Review (p. 423)

41. BE 2BD 2(6) 4;

3

3

BD BE ED

6 4 ED

2 ED

42. BE 2BD 2(33) 22;

3

3

BD BE ED

33 22 ED

11 ED

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43. BE 2BD 2(52) 342;

3

3

3

BD BE ED

52 342 ED 3

171 ED 3

8.2 Algebra Skills (p. 423)

44. 5 5 46. 48 48 48. 13.2 13.2 50. 0.001 0.001

45. 11 11 47. 0 0 49. 2 2 51. 1.11 1.11

Quiz 1 (p. 423)

1. Not regular; the polygon is equilateral but not equiangular. 2. Regular; the polygon is both equilateral and equiangular. 3. Not regular; the polygon is neither equilateral nor

equiangular. 4. (n 2) 180 (5 2) 180 3 180 540;

ma 1 92 120 76 112 540 ma 1 400 540 ma 1 140

5. (n 2) 180 (6 2) 180 4 180 720; ma 1 140 100 120 140 100 720 ma 1 600 720 ma 1 120

6. ma 1 104 79 68 360 ma 1 251 360 ma 1 109

7. ma 1 93 74 92 360 ma 1 259 360 ma 1 101

8. ma 1 50 61 95 44 360 ma 1 250 360 ma 1 110

Lesson 8.3

8.3 Checkpoint (pp. 425?426)

1. A bh 11 11 121 m2

3. A bh 5.9 4.5 26.55 yd2

2. A bh 62 12 ft2

4. A bh 52 4b

13 m b

Geometry, Concepts and Skills

Chapter 8 Worked-Out Solution Key

121

Chapter 8 continued

5. A bh bh (7)(3) (7 4)(6 3) (7)(3) (3)(3) 21 9 30 in.2

6. A bh bh bh (4)(3) (12)(6 3) (3)(5 3) (4)(3) (12)(3) (3)(2) 12 36 6 54 m2

8.3 Guided Practice (p. 427)

1. rectangle 2. C; A bh (2x)(2x) 4x2 3. A; A bh (x)(x) x2 4. B; A bh (2x)(x) 2x2 5. True; the area of the polygon is

Area A Area B Area C. 6. False; the height of Rectangle A is 7 3 2 2 units. 7. True; the height of Rectangle C is 3 2 5 units.

8.3 Practice and Applications (pp. 427?429)

8. A bh 6 6 36 ft2 9. A bh 12 12 144 m2 10. A bh 20 20 400 in.2 11. A bh 5 2 10 cm2 12. A bh 6 7 42 yd2 13. A bh 12.1 5 60.5 m2

14.

2.2 cm

A bh 2.2 2.2 4.84 cm2

15.

11 m

4 m

A bh 4 11 44 m2

16.

8 ft

13 ft

A bh 13 8 104 ft2 17. A bh 14 14 196 m2 18. A bh 7 7 49 m2 19. A bh 9 9 81 m2

20. A bh

21. A bh

56 8h

54 b 18

7 in. h

3 cm b

22. A bh

33 6.6h

5 ft h

23. Yes. Since the perimeter is 28 feet, each side measures 28 4 7 feet, Area 72 49 square feet.

24. b 11 4 2 5 ft,

h 3 ft

25. b 11 2 4 2 3 ft,

h 6 ft

26. b 4 ft

h (6 2) 3 4 3 7 ft

27. A bh bh

(12 7)(5) (7)(10)

(5)(5) (7)(10)

25 70 95 m2

28. A bh bh

(4)(8 3) (4 5)(3)

(4)(5) (9)(3)

20 27 47 in.2

29. A bh bh

(16 7)(9) (7)(5)

(9)(9) (7)(5)

81 35 116 yd2

30. A bh bh bh

(4)(12) (18 4)(11 5) (18 4 10)(5)

(4)(12) (14)(6) (4)(5)

48 84 20 152 cm2

122

Geometry, Concepts and Skills

Chapter 8 Worked-Out Solution Key

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Chapter 8 continued

31. A bh bh

(450)(400) (450 175)(500 400)

(450)(400) (275)(100)

180,000 27,500

207,500 ft2

32. 207,500 ft2 431,5a6c 0reft2 4.76 acres

33. C $34 4.76 acres $57 4.76 acres

acre

acre

$161.84 $271.32

$433.16

8.3 Standardized Test Practice (p. 429)

34. a. A bh bh

7x 6x

13x

b. 13x 65

x 5 units

c.

7

5

6

5

8.3 Mixed Review (p. 429)

35. C; C**E** *A**E* (Diagonals of a g bisect each other.)

36. A; C**D** *A**B* (Opposite sides of a g are .)

37. D; a ABD a CDB (If two parallel lines are cut by a transversal, then alternate interior angles are congruent.)

38. B; a CBA a ADC (Opposite angles of a g are .)

39. Yes; a U a R; also, the ratios of the sides that include a U and a R are equal.

shorter sides:

6 15

16533

2 5

longer sides:

10 25

1205 55

2 5

So, T SUT T PRQ by the SAS Similarity Theorem.

40.

No; shortest sides:

9 6

96 33

3 2

longest sides:

18 10

1180 22

9 5

remaining sides:

10 8

18022

5 4

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8.3 Algebra Skills (p. 429)

41. 8 18 43. 10 0 45. 2.44 2.04

42. 2459 2495 44. 1.12 1.01 46. 0.75 0.7

Lesson 8.4

8.4 Activity (p. 430)

1. yes 2. The area of the triangle is half the area of the rectangle. 3. Answers will vary. 4. A 1bh

2 5. A 1(14)(6) 42 ft2

2

8.4 Checkpoint (p. 433)

1. A 1bh 1(9)(8) 36 in.2 22

2. A 1bh 1(12)(7) 42 yd2 22

3. A 1bh 1(15)(16) 120 cm2 22

4.

A 1bh

2

84 1b(14) 2

168 14b

12 in. b

8.4 Guided Practice (p. 434)

1. base 9ft, height 5 ft

2.

3.

7

7

15

4.

15 7

15

8.4 Practice and Applications (pp. 434 ?437)

5. A 1bh 1(12)(7) 42 cm2 22

6. A 1bh 1(7)(6) 21 ft2 22

7. A 1bh 1(5)(3) 15 7.5 yd2

22

2

8. A 1bh 1(9)(4) 18 m2 22

Geometry, Concepts and Skills

Chapter 8 Worked-Out Solution Key

123

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