Geomtry (E) Name: ___________________________________Spring Final Exam Practice 2016 Period: ____1. Solve for x and y.

x

2y 2x 3y +5

2. Find the midpoints of all 3 sides of a triangle with vertices at A(3,11), B(12,-4), and C(1,-8).

3. Find the lengths of all 3 sides of a triangle with vertices at A(3,11), B(12,-4), and C(1,-8).

Fill in the blank with the most specific quadrilateral.

4. The diagonals of _____________________ are perpendicular bisectors each other.

5. A parallelogram with one set of consecutive sides congruent and a right angle is a ________________.

6. One set of parallel sides and lower base angles congruent is an ________________________.

Complete the following with Always, Sometimes or Never

7. A square is ______________ a parallelogram.

8. A rhombus is _____________ a kite.

9. A pentagon is ________________ a quadrilateral.

10. Find the perimeter of the kite

11. If AB bisects DBF and DF=16, find the value of x.

Answer the following questions as always, sometimes, or never true.12._____________ Two squares are similar.

13._____________ A square is a rectangle.

14._____________ If the diagonals of a quadrilateral bisect each other,

Simplify the following radicals

16. 17. 18.

19. 20. 21.

JK

LM

13 ft5 ft

SD = 15, DA = 7. Find OD ST = 13, IS = 4. Find AS. DA = 9, SO = 6. Find SA

22. What type of triangles are formed from the given sides?

a. 8 in, 15 in, 17 in b. 16 in, 5 in, 12 in

23. What is the area of rectangle JKLM?

24. Find the area of the shaded region in terms of π.

25. A 12-foot ladder is placed against the side of a building as shown in Figure 1 below. The bottom of the ladder is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, the ladder is moved 3 feet closer to the base of

5 ft

12 ft

Figure 28 ft

12 ft

Figure 1

the building as shown in Figure 2. How much higher does the ladder now reach? Leave your answer in the form that makes the most sense according to the situation. (5 points)

26

. Fill in the blanks for the table to the left. Leave answer in terms of π (1 point each)

27. Find A and arc AB if arc AC is 100°.

Angle A =_____ Arc AB =_____

Circumference Radius Diameter

30

15

40

28. Given D = (-1,3) and C = (-1,2), find DC 29. Find the distance between (2,-1) and (7,-2)

30. Find the perimeter of a triangle with points at (2, 5), (0,7), and (-3,0).

31. a.) Find the radius of the circle below. b.) Write an equation for the circle.

32. Given the following measurements, where A and B are the legs of the triangle and C is the hypotenuse, complete the chart.

35. Find the lengths of and . 36. Find the lengths of and .

A (leg) B(leg) C (hypotenuse)8 1710 2430 5014 28

3 54 7.5

37. Given: Circle w/ diameter

Tangents and

Secants and

,

,

Find the following measures (All answers in degrees).

a. ______

b. ______

c. ______

d. ______

e. ______

f. ______

g. ______

h. ______

i. ______

j. ______

k.) ______

38. a. If two sides of a triangle are 6 and 14, what are the restrictions on the third side?

b. 3 and 4 are two sides of a right triangle. What are the two possibilities for the third side?

39. 9 and 1 are the lengths of the legs of a right triangle. What is the length of the hypotenuse?

40. a. If RECT is a rectangle and EC = 3, find the lengths of TC and TE.

b. What is the area of RECT?

41. Solve the following equations for x. Round your answer to the nearest tenth.

a. b. c.

42. GD = 24 and m D = 12°. Find GF to the nearest tenth. 43. b = 2 and m A = 86°. Find a to the nearest thousandth.

Find ALL of the sides and angles to the triangles below. Round any decimal answers to the nearest tenth.

44. JL = 11 and m J = 12°. 45. S is a right angle. TR = 12 and m R = 23°.

46. A regular pentagon has an apothem of 6.2 m. Find the perimeter of the pentagon.

47. a. and are tangent segments to . Briefly explain why if , .

b. Given the diameter of is 28 and , what is the perimeter of quadrilateral PAWB?

48. In the picture on the right, find the four missing values.

h = _____

g = _____

f = _____

j = _____

49. Find arc w

50. Given: Circle M, CD = 20, and MF = 18

a. Find the distance from CD to the center of the circle.

b. If MG = 7.9 is AB = CD?

51. Y and K are on . m YSK = 137°. If the area of is , then:

a. What is the diameter of ? b. What is the area of ?

52. If AE = 10, DB = 24, and CE = 8. Find BE. 53. If AE = 11, DE = 3, and CB = 10. Find BE.

54. If AB = 22 and BC = 17. Find CD.

55. Points A, B, and C all lie on circle O. If is a diameter, , and , find .

56. Given the following angle measurements, find the measure of all 4 angles in the inscribed quadrilateral MATH. Note: The figure is not necessarily drawn to scale.

For problems 57-65, find the area of each figure.

57. 58.

59.

60. Find the area of the shaded region between the two circles 61. Find the area of the figure below. Assume if their radii are 8 and 2. Leave your answer in terms of π. right angles.

62. If the area of the trapezoid below is 98 cm2 and the height is 7 cm, find the length of .

Both #63 and #64 should be expressed in simplest radical form.

63. Square SQRE with . 64. Rectangle RECT with and .

65. What is the area of a triangle with sides 7, 9, and 13?

66. What is the area of an inscribed quadrilateral with consecutive sides with lengths of 7, 8, 6, and 10?

67. What is the area of if , , and ?

68. Find the area of a regular hexagon with a semiperimeter of 60.

69. A square is circumscribed by a circle of radius 40 feet. What is the area of the square?

70. In the picture a=2 cm, b=6 cm, c=6 cm, and d=2 cm. What is the area of the middle stripe? You may assume right angles.

71. Find the area of an equilateral triangle with a perimeter of 45 in.

72. Write the equation for a circle with center at the origin and radius of 10.

73. Write the equation for a circle with center at and diameter of 14.

74. What is the radius and the coordinates of the center of a circle with equation .

75. Write the equation of a circle that has a diameter with endpoints at and .

76. Find the surface area and volume of the sphere with a diameter of 18.

77. Find the volume only of a regular triangular pyramid with a base perimeter of 30 and an altitude of 12.

78. Find the surface area and volume of a regular hexagonal prism with base perimeter of 72 and height of 10.

79. Find the surface area and volume of a cone with radius of 19 and slant height of 10.

80. Find the surface area and volume of a rectangular prism with length of 5, width of 6, and height of 2.

81. Find the surface area and volume of a cylinder with base diameter of 22 and height of 5.