Geometry 2nd

Semester Review Name: ____________________

2014

1.7&4.1

Use the figure for Exercises 1–3.

The figure in the plane at right shows the preimage in the transformation

ABCD → A’B’C’D’. Match the number of the image (below) with the

name of the correct transformation.

1. rotation _______ 2. translation _______ 3. reflection _______

4. A figure has vertices at D(-2, 1), E(-3, 3), and F(0, 3).

After a transformation, the image of the figure has

vertices at D(-1, -2), E(-3, -3), and F(-3, 0).

Draw the preimage and the image. Then identify

the transformation.

____________________________________

Apply the transformation M to the polygon with the given vertices. Identify and describe the transformation.

5.M: (x, y) (x - 2, y - 3)

A(-2, -1), C(2, -4)

_____________________________________

6. M: (x, y) (2x, 2y)

E(-2, 2), F(1, 1), G(2, 2)

____________________________________

7. What rule (coordinate notation) would you use to translate a figure in the coordinate plane 2

units to the right and 3 units down?

7.1

Identify the pairs of congruent corresponding angles and the corresponding sides.

8.

__________________________________________________________________

Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. If not,

explain why not.

9. parallelograms EFGH and TUVW 10. ∆CDE and ∆LMN

____________________________________ _____________________________________

____________________________________ _____________________________________

Tell whether the polygons must be similar based on the information given in the figures.

11.

12.

7.2

Apply the dilation D to the polygon with the given vertices. Describe the dilation.

13.D: (x, y) (1.5x, 1.5y)

G(-4, 1), H(-2, 1), J(-2, 6), K(-4, 6)

____________________________________

14. D: (x, y) ( 12

x, 12

y)

P(-6, 8), Q(0, 6), R( –4, 2)

____________________________________

7.3

Explain why the triangles are similar and write a similarity statement.

15.

_________________________________________________________________________

_________________________________________________________________________

For Exercises 3 and 4, verify that the triangles are similar. Explain why.

16. ∆JLK and ∆JMN 17. ∆PQR and ∆UTS

____________________________________ _____________________________________

____________________________________ _____________________________________

____________________________________ _____________________________________

7.4

Find each length.

18. BH _______________________ 19.MV ________________________

Verify that the given segments are parallel.

20.WX and DE

_________________________________________________

_________________________________________________

________________________________________________________________________________

Find each length.

21. SR and RQ _____________________ 22. BE and DE ___________________

7.5

Given that DEFG WXYZ, find each of the following.

23.perimeter of WXYZ ________________________

24.area of WXYZ __________________________

8.2

Write each trigonometric

ratio as a simplified fraction and as a decimal rounded to

the nearest hundredth.

25.sin A 26. cos B 27. tan B

______________________ ______________________ ______________________

Use special right triangles to write each trigonometric ratio as a simplified fraction.

28.sin 30° ________ 29. cos 30° ________ 30. tan 45° ________

31. tan 30° ________ 32. cos 45° ________ 33. tan 60° ________

Use a calculator to find each trigonometric ratio. Round to the nearest hundredth.

34. sin 64° ________ 35. cos 58° ________ 36. tan 15° ________

Find each length. Round to the nearest hundredth.

37.

38.

XZ _____________ HI _____________

8.2 Extension

39. Fill in the chart below:

Find the value of x and/or y in each figure. Give your answer in simplest radical form.

40.

x= _____________________

41.

y=_____________________

8.3

Use the given trigonometric ratio to determine which angle of the

triangle is ∠A.

42. 8

sin17

A ________ 43. 15

cos17

A ________ 44. 15

tan8

A ________

Use a calculator to find each angle measure to the nearest degree.

45. sin-1

(0.82) ________ 46.

1 11cos

12 ________ 47. tan

-1 (5.03) ________

Find the unknown measures. Round lengths to the nearest hundredth and angle measures

to the nearest degree.

48.

49.

______________________ ______________________

_______________________ ______________________

8.4

Marco breeds and trains homing pigeons on the roof

of his building. Classify each angle as an angle of

elevation or an angle of depression.

50. 1 _____________________

51. 2 _____________________

52. 3 _____________________

53. 4 _____________________

Lindsey shouts down to Pete from her third-story window.

54.Lindsey is 9.2 meters up, and the angle of depression from

Lindsey to Pete is 79˚. Find the distance from Pete to the base

of the building to the nearest tenth of a meter.

______________________

55.To see Lindsey better, Pete walks out into the street so he is

4.3 meters from the base of the building. Find the angle of

depression from Lindsey to Pete to the nearest degree.

______________________

12.1

Identify each line or segment that intersects each circle.

56.

____________________________________

____________________________________

Find the length of each radius. Identify the point of tangency and write the

equation of the tangent line at this point.

57.

58.

____________________________________ _____________________________________

____________________________________ _____________________________________

____________________________________ _____________________________________

In Exercises 6 and 7, EF and EG are tangent to .H Find EF.

59.

60.

____________________________________ _____________________________________ 12.2

Find each measure.

61.

62.

mQS _____________ mHG __________________ _____________

mRQT _____________ mFEH _________________ _____________

63.

,L E and ∠CBD ∠FEG.

Find FG. ___________

Find each length. Round to the nearest tenth.

64.

65.

ZY __________________________________ EG _________________________________ 12.3

Find the area of each sector. Give your answer in terms of and rounded to

the nearest hundredth.

66.

sector BAC _________________

67.The speedometer needle in Ignacio’s car is 2 inches long. The needle

sweeps out a 130° sector during acceleration from 0 to 60 mi/h. Find

the area of this sector. Round to the nearest hundredth. _________________

Find each arc length. Give your answer in terms of and rounded to the

nearest hundredth.

68. 69.

____________________________________ _____________________________________

70. an arc with measure 45° in a circle with radius 2 mi _________________

71. an arc with measure 120° in a circle with radius 15 mm _________________

12.3 Extension

72. Convert each measure from degrees to radians.

a. 215° b. 25°

73. Convert each measure from radians to degrees.

a. 6

5

radians b.

3

5

radians

12.4

74. If a quadrilateral is inscribed in a circle, then its opposite angles are _____________________.

75. If inscribed angles of a circle intercept the same arc or are

subtended by the same chord or arc, then the angles are _____________________.

76. The measure of an inscribed angle is _____________________ the measure of its intercepted arc.

77. An inscribed angle subtends a semicircle if and only if the angle is a _____________________.

Find each measure.

78. m∠BAC = __________

mFE __________

Find each value.

79. x = __________ 80. z = __________

Find the angle measures of each inscribed quadrilateral.

81. m∠B = __________ .

m∠C = __________

m∠D = __________

m∠E = __________

82. Lyla has not learned how to stop on ice skates yet, so she just

skates straight across the circular rink until she hits a wall. She

starts at P, turns 75° at Q, and turns 100° at R. Find how many

degrees Iyla will turn at S to get back to her starting point.

_________________________

12.5

Find each measure.

83. m∠RPS = ________ 84. m∠YUX = _______

Find the value of x.

86. The figure shows a spinning wheel. The large wheel is turned

by hand or with a foot trundle. A belt attaches to a small bobbin

that turns very quickly. The bobbin twists raw materials into

thread, twine, or yarn. Each pair of spokes intercepts a

30° arc. Find the value of x.

85._________________

__

______________________________________

___

12.7

Write the equation of each circle.

87. X centered at the origin with radius 10 ______________________________________

88. O centered at the origin that passes

through (9, -2) ______________________________________

89. F with center F(11, 4) that passes

through (-2, 5). ______________________________________

Graph each equation.

90. (x - 1)2 (y - 1)

2 = 16

Crater Lake in Oregon is a roughly circular lake. The lake basin

formed about 7000 years ago when the top of a volcano exploded

in an immense explosion. Hillman Peak, Garfield Peak, and Cloudcap

are three mountain peaks on the rim of the lake. The peaks are

located in a coordinate plane at H(-4, 1), G(-2, -3), and C(5, -2).

91. Find the coordinates of the center of the lake.

____________________________________

10.1&10.2

Find each measurement.

92.

93.

the perimeter of the rectangle in which the area of the square

A = 2xy mi2

____________________________________ ______________________________________

94. the height of a parallelogram in which A = 96 cm2 and b = 8x cm ___________________

95.

96.

b1 of the trapezoid in which A = 4x2 in

2 the area of the triangle

____________________________________ _____________________________________

97. the area of a trapezoid in which b1 = 3a km, b2 = 6a km, and h = (10 - 4c) km

____________________________________

98.

99.

the perimeter of the kite in which the area of the rhombus

A = 49.92 yd2

____________________________________ _____________________________________

Find each measurement. Give your answers in terms of .

100.

the area of V

____________________________________

Stella wants to cover a tabletop with nickels, dimes, or quarters. She decides to find which

coin would cost the least to use.

101.Stella measures the diameters of a nickel, a dime, and a quarter. They are

21.2 mm, 17.8 mm, and 24.5 mm. Find the areas of the nickel, the dime, and

the quarter. Round to the nearest tenth.

________________________________________________________________________________

Find the area of each regular polygon. Round to the nearest tenth.

102.

103.

____________________________________ _____________________________________

11.1

For Exercises 1–4, match the given parts of the figure to the names.

104.vertex ______ a. triangle PUT

105.edge ______ b. point T

106.face ______ c. pentagon PQRST

107.base ______ d. segment PU

Classify each figure. Name the vertices, edges, and bases.

Type of figure: ________________________

Vertices: _____________________________

Edges: _______________________________

108.

Tell what kind of three-dimensional figure can be made from the given net.

109. 110.

____________________________________ _____________________________________

Tell what kind of shape each cross section makes.

111. 112.

____________________________________ _____________________________________

11.2

Find the volume of each prism. Round to the nearest tenth if necessary.

113. 114.

the oblique rectangular prism the regular octagonal prism

____________________________________ _____________________________________

Find the volume of each cylinder. Give your answers both in terms of 𝛑 and

rounded to the nearest tenth.

115.

____________________________________

116.CDs have the dimensions shown in the figure. Each CD

is 1 mm thick. Find the volume in cubic centimeters of a

stack of 25 CDs. Round to the nearest tenth.

________________________

Find the volume of each composite figure. Round to the nearest tenth.

117.

11.3&11.4

Write each formula.

118. volume of a pyramid with base area B and height h _____________________

119. volume of a cone with radius r and height h _____________________

Find the volume of each pyramid.

120. 121.

the rectangular pyramid the right triangular pyramid

____________________________________ _____________________________________

Find the volume of each cone. Give your answers both in terms of 𝛑 and rounded to the

nearest tenth.

122.

____________________________________

123. An ant lion is an insect that digs cone-shaped pits in loose

dirt to trap ants. When an ant tumbles down into the pit,

the ant lion eats it. A typical ant lion pit has a radius of

1 inch and a depth of 2 inches. Find the volume of dirt

the ant lion moved to dig its hole. Round to the nearest tenth.

____________________________________

Find each measurement. Give your answers in terms of 𝛑.

124. 125.

the volume of the hemisphere the volume of the sphere

____________________________________ _____________________________________

________________________________