Similar Polygons GEOMETRY LESSON 8-2

(For help, go to Lessons 4-1 and 8-1.)

Solve each proportion.

1.

ABC

2. 3 = x 4

8

HIJ. Name three pairs of congruent sides.

3. 2 = 8 x

24

4. x = 1 9

3

5. 10 = 2 25

x

Similar Polygons GEOMETRY LESSON 8-2

Solutions 1.Choose pairs of letters in the same position on each part of the congruence statement

ABC

HIJ: AB

2. Multiply both sides of 3 = x by 8: x = 3 4

8

4

HI, AC 8 = 3 1 1

HJ, BC 2 =6 1

3. Simplify 8 in 2 = 8 : 2 = 1 ; use the Cross Product Property: 24

x

24

x

3

(1)x = (2)(3); simplify: x = 6

4. Multiply both sides of x = 1 by 9: x = 1 9

3

3

9 = 9 =3 1 3

5. Simplify 10 in 10 = 2 : 2 = 2 ; use the Cross Product Property: 25

25

x

5

x

(2)x = (5)(2); simplify: 2x = 10; divide by 2: x = 5

IJ

Similar Polygons GEOMETRY LESSON 8-2

ABC ~

XYZ Complete each statement. a. m B = ? b. BC = ? YZ

XZ

Two polygons are similar if (1) corresponding angles are congruent and (2) corresponding sides are proportional. a.

B Y and m Y = 78, so m B = 78 because congruent angles have the same measure.

b. Because AC corresponds to XZ, BC = AC. YZ

XZ

Similar Polygons GEOMETRY LESSON 8-2

Determine whether the parallelograms are similar. Explain.

Check that the corresponding sides are proportional. AB 2 = JK 4

BC 1 = KL 2

CD 2 = LM 4

DA 1 = MJ 2

Corresponding sides of the two parallelograms are proportional. Check that corresponding angles are congruent.

B corresponds to congruent.

K, but m B =/ m K, so corresponding angles are not

Although corresponding sides are proportional, the parallelograms are not similar because the corresponding angles are not congruent.

Similar Polygons GEOMETRY LESSON 8-2

If

Because AC BC = YZ XZ x = 12 40 30

x = 12 30

x = 16

40

ABC ~

ABC ~

YXZ, find the value of x.

YXZ, you can write and solve a proportion.

Similar Polygons GEOMETRY LESSON 8-2

A painting is 24 in. wide by 36 in. long. The length of a postcard reduction of the painting is 6 in. How wide is the postcard? The postcard and the painting are similar rectangles, so you can write a proportion. Let x represent the width of the postcard. Postcard width = postcard length Painting width painting length x 6 = 24 36 6

x = 36

24

x=4 The postcard is 4 in. wide.

Similar Polygons GEOMETRY LESSON 8-2

The dimensions of a rectangular tabletop are in the Golden Ratio. The shorter side is 40 in. Find the longer side. Let 40

represent the longer side of the tabletop.

= 1.1618 1

= 64.72

The table is about 65 in. long.

Similar Polygons GEOMETRY LESSON 8-2

Pages 425-429 Exercises 1.

JHY

2. 3.

9. yes; KLMJ ~ PQNO; 3

17. 6.6 in. by 11 in.

R

5 10. yes; ABCD ~ FGHE; 4 5

18. 3.6 in. by 6 in.

JXY

11. No; corr.

19. 70 mm

s

are not

7 5

4. HY

12. yes;

5. JT

13. x = 4; y = 3

21. 2 : 3

6. HY

14. x = 20; y = 17.5; z = 7.5

22. 3 : 2

7. no;

20 36 = / 30 52

8. yes; QRST ~ XWZY; 3

4

ABC ~ FED;

.

15. x = 16; y = 4.5; z = 7.5 16. x = 6; y = 8; z = 10

20. 54 in. by 87.37 in.

23. 50 24. 50

Similar Polygons GEOMETRY LESSON 8-2

25. 70

31. 20 ft

2

26. 3

s

of

41. sides of 2 cm; 60° and 120°

s

of

32. x = 60, y = 25

27. 7.5 m

33. 2.6 cm

28. 5.6 m

34. 3 : 4

29. Yes; corr. sides are

40. sides of 2 cm; 60° and 120°

s

and

s

of

43. sides of 0.8 cm; 60° and 120°

s

of

35. 3 : 1

. 36. 2 : 1

30. equal sign, similarity symbol; Answers may vary. Sample: figures are similar with = areas.

42. sides of 3.2 cm; 60° and 120°

37. 1 : 2

44. sides of 1 cm; 60° and 120°

s

of

45. sides of 3 cm; 60° and 120°

s

of

38. 4 : 3 39. 2 : 3

Similar Polygons GEOMETRY LESSON 8-2

46. 16.2 in.

47. 6.2 in. 48. No; corr. sides are not in proportion. 49. Yes; explanations may vary. Sample: The ratios of radii, diameters, and circumferences of 2 circles are =.

51. a. (1) Corr. sides of ~ polygons are proport. (2) Subst. (3) Cross-Product Prop. (4) Subtr. Prop.

52. a. 21, 34, 55, 89, 144, 233, 377 b. 1.6; 1.625; 1.6154; 1.6190; 1.6176; 1.6182; 1.6180; 1.6181; 1.6180 c. The ratios get closer to the golden ratio. 53. D

b. Length cannot be negative.

54. C

c. 1.6180

55. A

Similar Polygons GEOMETRY LESSON 8-2

56. [2] a. 12 cm

61. no; only one pair of || sides

b. m KLM = 38 [1] incorrect length OR incorrect angle measure

62. Yes; both pairs of sides are ||. 63.

CEA, BCD

57. 7y 64. BD, FA

58. 7 9

65. 8

59. y + 9 9

60. Yes; the diagonals bisect each other.

66. 69

FED,

Similar Polygons GEOMETRY LESSON 8-2

Use the trapezoids below for Exercises 1â&#x20AC;&#x201C;3. DFHN ~ BMLP. Complete each statement. 1. m H = 2. x =

?

3. m D =

74

? 49 ?

99

4. A 4-in. by 6-in. drawing is enlarged to fit on a poster that measures 20 in. by 24 in. What are the dimensions of the largest drawing possible? 16 in. by 24 in. 5. A rectangle with a perimeter 20 cm has a side 4 cm long. A rectangle with perimeter 40 cm has a side 8 cm long. Determine whether the rectangles are similar. If they are, give the similarity ratio. If they are not, explain. yes; 1 : 2 6. The longer side of the golden rectangle is 20 ft. Find the length of the shorter side, rounded to the nearest tenth. 12.4 ft

geo book 8.2 key
geo book 8.2 key

geo book 8.2 key