Honors Geometry



Honors Geometry Name _____________________________________________ Hour:

Sem. 2 Final Exam Review Chapters 6-12

Directions: Show all your work wherever possible. Insufficient work will result in a loss of credit.

This completed packet must be turned in on the day of your exam.

Check and correct each problem for maximum credit.

15. 1.

2. The angle bisectors of a triangle are concurrent

at a point called the _____.

3. The incenter of a triangle is equidistant from

the three ____ of the triangle.

4. The medians of a triangle are concurrent.

Their common point is the ____.

a. centroid c. orthocenter

b. incenter d. d. circumcenter

5.

6.

7.

[pic]

8.

9.

10.

11.

12.

13.

| |A. 3, 5, 9 B. 1, 2, 2 |C. |6, 9, 12 D. 5, 12, 13 |

| | | | |

| | | | |

14.

16. Find the length of the leg of this right triangle.

Give an approximation to 3 decimal places.

17. How long is a string reaching from the top of a

13-ft pole to a point on the ground that is 7 ft

from the base of the pole?

18. The city commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram at the right. The construction cost has been estimated at $110 per linear foot. Find the estimated cost for constructing the street. (1 mile = 5280 ft)

19. If a, b, and c are sides of a right triangle,

which of the following are also sides of a right triangle?

| |A. The square root of each length ([pic]) B. Twice|

| |the length of each side (2a, 2b, 2c) |

| | |

| |C. Four more than each length (a + 4, b + 4, c + 4) |

| |D. The square of each length |

20. A set of Pythagorean triples is _____.

21. Mark went for a mountain-bike ride in a relatively flat, wooded area. He rode for 7 km in one direction, then turned and peddled 5 km in another. Finally he turned and rode 7 km in yet another direction. Stopping, Mark took out a map and drew his path. Could Mark be back at his starting point? Could his path be a right triangle?

22. For each set of numbers, determine whether the numbers represent the lengths of the sides of an acute triangle, a right triangle, an obtuse triangle, or no triangle.

a. [pic] b. 3, 4, 5

c. 6, 9, 12 d. 3.2, 4.2, 5.2

23. Which of the following cannot be the lengths of a

30°-60°-90° triangle?

A. [pic] B. [pic]

C. [pic] D. [pic]

24. An equilateral triangle has side lengths of 10.

The exact length of its altitude is _____.

25. a. Find the exact value of x and y.

b. Find the exact perimeter of ∆ABC.

26. Find tan S.

27. Explain how a tangent ratio can be used to find the

height of the building in the figure below.

Find the height of the building when m(A = 35(.

28. A slide 4.1 m long makes an angle of 27° with the ground. How high is the top of the slide above the ground?

29. Liola drives 16 km up a hill that is at a grade of 10°.

What horizontal distance, to the nearest tenth of

kilometer, has she covered?

30. Find the missing side lengths for x and y.

Give an exact answer.

31. Find the missing side lengths for x and y.

Give an exact answer.

32. Find the value of x in the picture below.

(The figure is not drawn to scale.)

33. What is the measure of each interior

angle in a regular octagon?

34. Find each unknown angle measure.

35.

36. Given: UVWX is a parallelogram, m(WXV = 17(,

m(WVX = 29(, XW = 41, UX = 24, and UY = 15.

a. Find m(WVU.

b. Find WV.

c. Find m(XUV.

d. Find UW.

37. Given: FGHJ is a parallelogram,

m(JHG = 68°, JH = 34, GH = 19

a. Find m(FJH.

b. Find JF.

c. Find m(GFJ.

d. Find FG.

38. Given: Trapezoid ABCD with midsegment [pic].

If [pic]and [pic], find the length of [pic].

39. Which statement is false?

| |A. Every square is a parallelogram. |

| |B. Some rhombuses are rectangles. |

| |C. Every rhombus is a quadrilateral. |

| |D. Every parallelogram is a rhombus. |

40. Which statement is false?

| |A. If a quadrilateral is a square, then it is not a kite. |

| |B. Some parallelograms are rhombuses. |

| |C. All parallelograms are quadrilaterals. |

| |D. If a quadrilateral is a rectangle, then it is a kite. |

41. List all of the important characteristics of each quadrilateral. Include a sketch for each.

a. Square:

b. Rectangle:

c. Parallelogram:

d. Rhombus:

e. Trapezoid

f. Kite:

42. The circle is circumscribed by the pentagon as shown (not drawn to scale). If QZ = 10, YX = 9, XW = 13, UW = 16, and SU = 17, find the perimeter of the pentagon.

43. Given RP = 22, RA = 6, and [pic]is tangent

to circle R at Q, find PQ.

44. In the diagram, [pic] is a radius of circle R.

Is [pic] tangent to circle R? Explain.

45. Given: In (O, mBAC = 290(. Find m(B.

46. Find mDBC in (P.

47. Given circle O with radius 5 and OC = 3. Find the length of [pic].

48. The diagram shows a cross-section of a large storm

drain pipe with a small amount of standing water.

The distance across the surface of the water is

48 inches and the water is 4.25 inches deep at its

deepest point. To the nearest inch, what is the

diameter of the storm drain pipe?

49. Given: m(IED = 116° and m(JFG = 100°

Find the measure of each numbered angle.

50. Given: (D; [pic] bisects (ADC.

Prove: AB ( CB (by using a triangle congruence theorem)

Statements Reasons

51. Find mBC and m(D.

52. mAB = 82( and mCD = 30(. Find m(DOC.

53. A park maintenance person stands 15 m from a

circular monument. If you draw two tangents from

the maintenance person to each side of the monument,

they make an angle of 37°. What is the measure of the

arc created where the lines intersect the monument?

54. Find the value of x if mAB = 20( and mCD = 62(.

55. Find the value of x.

56. Given: [pic]

57. Prove: [pic]

Statements Reasons

58. Write the standard equation of a

circle with center (–3, –4) and radius 6.

59. Write the standard equation of a circle with

center (–3, 5) that contains the point (1, 8).

60. A rectangular garden 42 feet by 20 feet is surrounded by a walkway of uniform width. If the total area of the garden and walkway is 1248 square feet, the width of the walkway is ? .

61. Find the area of the parallelogram.

62. Find the area of the triangle. (Not drawn to scale)

63. Find the area of the quadrilateral. (Not drawn to scale)

64. Find the area of the region below.

65. Explain how to find the area of a rhombus whose

side length and angle measures are given.

66. The ratio of the side lengths of two regular hexagons is 4 to 9.

If the area of the smaller hexagon is 16 square units,

then the area of the larger hexagon is ? .

67. Figure P is similar to figure Q. The area of P is 16 in2. If the ratio of corresponding lengths of P to Q is 1: 3, what is the area of Q?

68. Two similar trapezoids have areas 363 cm2

and 192 cm2. Find the ratio of similarity.

69. A car has 20-inch diameter wheels. If the wheels revolved three times after the brakes were applied, the stopping distance was approximately ? .

70. The needle of the scale in the bulk food section of a

supermarket is 25 centimeters long. What distance

does the tip of the needle travel when it rotates ⅔

of the way around the dial, rounded to the nearest tenth?

71. The radius of the circle is[pic]. The distance from the

center to the chord is 1. If the measure of AB is 90°,

what is the exact area of the shaded region?

72. Each circle is tangent to the other two.

If the diameter of the large circle is 12,

the area of the shaded region is ? .

73. Find the area of a regular decagon with

radius 7 cm. Round to the nearest tenth.

74. What is the perimeter of the regular

hexagon to the nearest inch?

75. Find the exact surface area of the right cylinder below.

76. Find the lateral area of the

regular pyramid below.

77. Find the exact surface area of the right cone below.

78. Find the exact volume of a cylinder that

has a height of 18 inches and a radius of 8 inches.

79. Find the volume of the right prism below.

80. Find the volume of the pyramid below.

81. A cylindrical vase has a diameter of 4 inches and a height of 14 inches. You place some marbles at the

bottom of the vase that take up about 38 cubic inches. You fill the vase with water up to 3 inches from the top. Write an expression you can use to determine the approximate volume of water in the vase.

82. Calculate the volume of the cone. Use ( ( 3.14.

83. A pyramid-shaped puzzle exactly fits its cubic storage box. The space between the puzzle and the sides of the box is filled with a light-weight plastic foam to help protect the puzzle during shipping. What is the volume of the foam?

84. What is the surface area of a

sphere with radius 4.7 feet?

85. Find the volume of a sphere 4 ft in diameter. Use ( ( 3.14 and round your answer to the nearest tenth.

86. The inside of an ice cream cone is filled

with ice cream and has radius 6 cm and

height 12 cm. Assuming that a half-scoop

of ice cream is in the shape of a hemisphere,

and that it fits perfectly on top of the cone

(same radius), find the total volume of ice cream.

Round your answer to the nearest tenth.

87. Find each unknown angle measure.

88. Find the value of x.

89. Define:

Law of Sines:

Law of Cosines

90. In ∆AUQ, m(U = 112(, QU = 88.1, and AU = 78.

Find m(Q.

91. In ∆CYE, YC = 90, YE = 78, and EC = 72.

Find m(E.

92. In ∆KBU, m(B = 73(, m(U = 85(, and UB = 22.4.

Find KB.

93. In ∆RKZ, KZ = 128.30, KR = 123.38,

and RZ = 53.32. Find m(Z.

94. John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33(. This particular tree grows at an angle of 83( with respect to the ground rather than vertically (90(). How tall is the tree?

1. X = 3

2. Incenter

3. Sides

4. A

5. 5

6. 125

7. a

8. x>3/4

9. [pic]

10. [pic]

11. D

12. C

13. [pic]

14. A

15. 12.329 units

16. [pic]ft

17. $3,386,617

18. B

19. D

20. Yes; No

21. a. right b. right c. obtuse d. acute

22. B

23. 5[pic] units

24. a. [pic] units

b. [pic] units

25. [pic]

26. [pic]; [pic].

So h = 150(tan 35() ( 150(0.7) or about 105 feet.

27. 1.86 m

28. 15.8 km

29. [pic]

30. x = 4, y = [pic]

31. 51

32. 135°

33. 56°, 84°, 92°, 128°

34. a. 46° b. 24 c. 134° d. 30

35. a. 112° b. 19 c. 68° d. 34

36. 20 units

37. D

38. D

39. a. Square: Four congruent sides, four right (congruent) angles, opposite sides parallel, congruent diagonals, diagonals are the perpendicular bisectors of each other.

b. Rectangle: Opposite sides congruent and parallel, four right (congruent) angles, congruent diagonals, diagonals bisect each other.

c. Parallelogram: Opposite sides congruent and parallel, opposite angles congruent, diagonals bisect each other.

d. Rhombus: Four congruent sides, opposite sides parallel, opposite angles congruent, diagonals are the perpendicular bisectors of each other.

e. Trapezoid: One pair of opposite sides parallel

f. Kite: Two pairs of adjacent sides congruent

40. 98 units

41. [pic]

42. No; for [pic] to be tangent to circle R, [pic]and[pic] would have to be perpendicular. Using the converse of the Pythagorean Theorem you find that 42 + 122 ( 132, therefore ∆RST is not a right triangle and[pic]and[pic]are not perpendicular.

43. 35°

44. 238°

45. 8 units

46. 140”

47. m(1 = 80(, m(2 =64(, m(3 = 100(, m(4 = 116(

48.

49. mBC = 80(, m(D = 40(

50. 26°

51. 143°

52. 41°

53. 16

54.

55. (x + 3)2 + (y + 4)2 = 36

56. (x + 3)2 + (y − 5)2 = 25

57. 3 ft

58. 680 sq. units

59. 14.4 cm2

60. 55 sq. units

61. 417 sq. unit

62. Sample answer: Draw the two diagonals of the rhombus, thus forming four congruent right

triangles whose acute angles have measures that are half those of the angles of the rhombus. Then use the sine or cosine function to find the lengths of the legs of these right triangles. Find the area of one triangle and multiply this area by 4 to get the area of the rhombus.

63. 81 sq. unit

64. 144 in2

65. 11 : 8

66. 188.5 in or ( 15.7 ft

67. 104.7 cm

68. [pic] un2

69. 18( un2

70. 144.0 cm2

71. 25.3 inches

72. [pic]

73. 336 ft2

74. 44( in2

75. 1152( in3

76. 60 ft3

77. 126 ft

78. ((2)2 (14 − 3) − 38 = 44( − 38 in3

79. 157 m3

80. 228.67 cm3

81. 277.6 ft2

82. 33.5 ft3

83. 904.8 cm3

84. 40(, 45(, 60(, 90(, 125(

85. 4

86. Law of Sines: [pic]

Law of Cosine: [pic]

[pic]

[pic]

87. 31.65(

88. 73.62(

89. 59.569 units

90. 72.64(

91. ( 60.6 feet

-----------------------

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Honors Geometry

Final Exam Review Answers page 1

|Statements |Reasons |

|1. (D; [pic] bisects (ADC |1. Given |

|2. Draw [pic] and [pic] |2. Two points determine a line |

|3. [pic] |3. Definition of circle |

|4. (1 ( (2 |4. Definition of angle bisector |

|5. ∆ADB ( ∆CDB |5. SAS ( |

|6. [pic] |6. CPCTC |

|7. AB ( CB |7. a, corresponding chords are congruent.two minor arcs are |

| |congruent if and o their |

|Statements |Reasons |

|1. [pic] |1. Given |

|2. (QUT ( (RUS |2. Vertical Angles Congruence Theorem |

|3. ( S ( (T |3. If two inscribed angles of a circle intercept |

| |the same arc, then the angles are congruent. |

|4. ∆QUT ( ∆RUS |4. AAS ( |

|5. [pic] |5. CPCTC |

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