Geometry Spring Final Review

  1. Draw a picture of a triangle reflection.
  1. Draw a picture of a trapezoid translation.
  1. ∆NPQ has vertices N(-3,-4), P(-8, 4), and Q(2, 1). If the triangle is rotated 90 degrees about the origin, what are the coordinates of P’ ?

Remember : (x,y)  (-y,x)

  1. Given A(3,2), B(6,3), C(6,7), D(-2,6) find A’B’C’D’ using vector .
  1. Find AB.
  1. The Washington Memorial has a height of 555 feet 5⅛ inches. If you made a scale drawing using the scale 1 in : 55 ft, what would be the height in the drawing?
  1. Rectangle DEFG and rectangle HJKL are similar. Find the similarity ratio.
  1. Find x.
  1. Given that two points on line m are P(8, 4) and Q(13, 7). Write a ratio of the slope of line m.
  1. Find the surface area of a cube with 11 inch edges.
  1. Find the scale factor that maps ∆ABC onto ∆A’B’C’
  1. Katie is making a table for her little sister’s doll house. She wants the table top to be similar to their real table top in their kitchen. Find the width of the miniature table top to the nearest tenth of a centimeter.
  1. Solve the proportion.
  1. Write the trigonometric ratio for cosJ as a fraction and reduce.
  1. Find TR. Round to the nearest whole number.
  1. Find the volume.
  1. Find the surface area.
  1. Find the lateral area in terms of π.
  1. What is the height of a right rectangular prism with surface area 1399.68 m2, length 10.8m, and width 14.4m?
  1. A rectangular swimming pool has a volume of 11,340 cubic feet, a depth of 12 feet, and a length of 63 feet. What is the width of the swimming pool?

Use this picture for #21-23

21. Describe .

22. Describe .

  1. Describe
  1. Find the length of .

25. What is the area of the sector POM in terms of π?

26. What is the length ofarc JL?

  1. What is the m LMN?
  1. What is the measure of arc PN?
  1. Find the value of x.
  1. Find the diameter of a sphere with volume

288 π in3.

  1. Find the volume of a sphere with diameter

42 feet. Give your answer in terms of π.

  1. Find the surface area of a sphere with a diameter of 26 km. Round to the nearest hundredths.
  1. Find mBPD.

34. Find the value of x and the length of each chord.

35. Write the equation of a circle with center

(-5, 7) and radius 6.

  1. Find the area of the parallelogram.

37. Find the area of in terms of .

38. Find the area of the trapezoid.

  1. Find the mA.

40. Find the value of x. Round to nearest hundredths.

41. Find the value of x. Round to nearest hundredths.

42. The central angle of an arc measures 12°. The radius of its circle is 30 inches. What is the length of the arc to the nearest quarter of an inch?

43. Find the area of a regular hexagon with side length 4 m. Round to the nearest tenth.

44. Find the geometric mean of 6 and 10.

45. Find the area of the composite figure.

46. Find the length of arc JK. Give your

Answer in terms of π.

47. What is m arc UV?

A. 70˚

B. 80˚

C. 100˚

D. 122˚

48. Which of these arcs has

a measure of 134˚ ?

A.arc FJ B. arc EG

C. arc DF D. arc DH

49.Tell whether the figure is a polygon. If it is, tell whether it is convex or concave.

A not a polygon

B polygon, convex

C polygon, concave

50. In the following parallelogram, find FI.

51. The measure of each exterior angle of a

regular octagon is .

52. The measure of each exterior angle of a

regular hexagon is .

53. The measure of each interior angle of a

regular octagon is .

54. Find the sum of the interior angle measures of a convex heptagon.

55. If DEFG is a square, find mDEG.


56. Given rectangle ABCD, if AC = 52, then

DX = .

57. For the trapezoid shown below, find the measure of the midsegment.

58. Identify the quadrilateral which has one pair of parallel sides.

59. Given parallelogram TAXI , mITA=4y+12 and mIXA=2y+48, find mIXA.

60. Given rhombus WXYZ and m1=27, find m5.

61. In the figure TAMU below, which angles are congruent?

62. In an isosceles trapezoid ABCD, leg AB=2y+7, base BC=10y+9, and leg CD =6y+5. Find y.

63. A regular polygon has all its sides and angles congruent.

  1. always
  2. sometimes
  3. never

64. One way to prove that a quadrilateral is a parallelogram is to show that:

a. it has one pair of congruent sides

b. it has one pair of parallel sides

c. the diagonals bisect each other

d. the diagonals are congruent

65. Give the most precise name for a regular quadrilateral.

66. In a square,

a. opposite angles are equal.

b. opposite sides are equal.

c. diagonals bisect the angles of the square.

d. all of these.

67. Which statement is true?

a. All rectangles are squares.

b. All quadrilaterals are parallelograms.

c. All parallelograms are quadrilaterals.

d. All quadrilaterals are squares.

68. If CDEF is a rectangle and CD=6, what is EF ?