,1/'-' Name: _

( Final Exam Practice for Geometry B\

1. Find the length of the leg of this right triangle. Give an approximation to 3 decimal places.

30

a. 8.062b. 17.748

c. 46.098d. 18.028

2. How long is a string reaching from the top of a13-ft pole to apoint on the ground that is 7 ft fromthe base of the pole+.-- .

a. J120 ft,J218 ft,.)208 ft

,JUO ft

b.

c./ d.

3. MBC is a right triangle. AB = __ .

A

~B

a. 4-J4i.2-J4i.4,JU164

b.

c.d.

4. For the triangle shown below, the PythagoreanTheorem states that

G

a. a2 +b2 =c2

b. a = b + cc. b2+c2=a2

d. a2 +b2 = c2

5. A set of Pythagorean triples is __ .

a. 3,5,9-b. 1, 1,2c. 6,9,12d. 5, 12, 13

6. - Which set of lengths cannot form a right triangle?

a. 11 mm, 24 mm, 26 mmb. 20 mm, 48 mID, 52 mmc. 5 mm, 12 rnm, 13 romd. 10 mm, 24 mID, 26 mm

1

7. If the side lengths of a triangle are 7, 4, and 9, thetriangle __ .

a. is an obtuse triangleb. is a right trianglec. is an acute triangled. cannot be formed

8. Choose the set that is the possible side lengths of aright triangle.

a. 2,2,3b. 2,2,~c. 3,4,5d. . 4,5,9

,-

9. For each set of numbers, determine whether thenumbers represent the lengths of the sides of anacute triangle, a right triangle, an obtuse triangle, orno triangle.

A. J38, 55, ,J13B.3,4,7C.6,9,12D. 3.2,4.2,5.2

10. A triangle has side lengths of 6, 9, and 11. Decidewhether it is an acute, right, or obtuse triangle.

11. A triangle has side lengths of7, 9, and 11. Decidewhether it is an acute, right, or obtuse triangle.

12. Classify a triangle with sides 10, 10, and 9 as acute,obtuse, or right.

13. Find a, b, and h.. ..

a~

6 48

a) a = 16, b = 56.9, c = 16.97 \

b) a = '16, b = 50.4, c = 16.97 \'c) a = 18, b = 56.9, c = 16:97dJ a = 18, b = 50.4, c = 17.76

14. Find the length of the altitude drawn to thehypotenuse.

a) 6b) 5c) 4d) 8

Use the diagram below.

15. QS is the geometric mean of Q P and_.

2

16. Find the value of the variabl~)~t4r(!4iagram.

~

.

. . -. -:.1 .i .. a

. 1_.

~~ __ ._'h~

I '', __ -IIr---- I

a) 13.85b) 14.46c) 15.75·d) 20.42-

17. Find the value ofx and y.

x = 14, Y = 40.6 ,

x = 16, Y = 40.4 .I

x = 14, Y = 38.2 !:x = 16, Y = 44.2

~<------y------->~.

18. In a 45°_45°_90° triangle, the ratio of the length ofthe hypotenuse to the length of a side is __ .

\.

a. 1:1b. ,J3:1

c. J2:1d. 2:1

19. Find the value of x and y.r.' ';..-" -:.\,

a) l x = 5-fL, Y'1lO

b) 'x = sB, v= 10c) x = 5.J3, Y = 100 .d) x = 51)3, Y = 100x

20. Find the value of x and y.,

a) x = 113, Y= 11

.~=11'Y:113.

600

22

21. Which of the following cannot be the lengths of a30°-60°-90° triangle?

7 14 7 r:a. 3'3'3",,3b. 11,22,11,J3c. 4,8,4-13d. 10,5, 10-13

22. An equilateral triangle has side lengths of 10. Thelength of its altitude is __ .

1O,J"5b. 5

550d. 5-13

a.

c.

23. Find the value of x.

a) 48 I~

b) lG4L,,To ~ c) 6-J2

d) 4V2

24. Find tan A for the right triangle below:

~:A 24 C

/\

'~,.~

3

25. A photographer shines a camera light at a particular painting forming an angle of 49° with the camera platform. Ifthe light is 53 feet from the wall where the painting hangs, how high above the platform is the painting?

x

53 ft

b. 1.15 fta. 0.87 ft c. 60.97 ft

27. Write cas B.26. Write sin B.

8

Ii 15 C

siY'B-==~\5 ~)a.j n 1S

b) \1 d) \s- -\5 8

28. Find sin P, cas P, tan P.

16

~----------------~ P3D

»:{

!

d. 46.07 ft

A 12 C

12a. -

13

b.5-1212

c. -5

d.5-13

'Sin P =:Cos-P=i::tu1P=

(

.••....

4

29. The cosine of LA is the ratio __

Aadj.

adj.b.

opp. hypod.

opp.a.hypo hypo c.

adj. adj.

30. Find the value of X, to the nearest whole number. (not drawn to scale)

a) 15.631

b) 12.42c) 5.07d) 4.85

~~13_ .~F ------E

3 1. Find x, to the nearest hundredth.

a) 11.54b) 5.14c) 9.71d) 10.07

x

i\

5

32. Use the diagram to find sin x as a fraction in simplest form.

24~

32

a.3445b.

33. Find cas B for the right triangle below:

4041

b. 940

a.

c.

d.409

(

d.

c. 941

34. Assume that LA is an acute angle and tan A =1.230. The measure of LA is

a. about 39.1 0

b. about 7.010

c. about 50.9°d. about 129.90

6

35. Solve for x to the nearest degree.

a. 20b. 22c. 70d. 68

36. Find the measure of the missing angle.

a) 1020 •

b) 92"

114" ? c) 11~d) 122"

37. Find x andy.

a) x = 96, Y= 720

b) x = 106, Y= 720

38. Find the sum of the measures of the interior anglesin the figure.

\.a) 5400.

b) 7200

c) 9000

d) 3600

39. The sum of the measures of the interior angles of aconvex pentagon is __ -a. 1800

b. 2700

c. 3600

d. 5400

40. What is the measure of each interior angle and eachexterior angle in a regular octagon?

Interior: ----~-------------Exterior: -------------------

{

\ •...

Find the value of x. (The figure may not be drawnto scale.)

41.

. a. 46b. 44c. 121d. 61

42. Find the measure of each exterior angle of a regularpolygon with 20 sides.a. 360°b. 162°c. 9°d. 18°

43. Find the measure of one of the interior angles of aregular polygon with eight sides.a. 135°b. 157.5°c. 45°d. 22:5°

Find each unknown angle measure.

a) 56, 94, 118,92

(,'i' ~ ]orw' b) 56,84, 128,92c) 56,84, 138,82d) 56, 94, 128, 82

44.

7

45. Find AM in the parallelogram if PN = 7 andMO= 14.

11{~----------------~

111:.- ---.;:» 0

46. For parallelogramPQLMbelow, ifmLPML = 87°,then mLPQL = _

ptt-------~ Q

M

a. mLPQMb. 93°c. 87°d. mL.QLM

47. Consecutive angles in a parallelogram are always

a. congruent anglesb. complementary anglesc. supplementary anglesd. vertical angles

48. Choose the statement that is NOT ALWAYS true.For any parallelogram _a. the diagonals bisect each otherb. opposite angles are congruentc. the diagonals are perpendiculard. opposite sides are congruent

49. Find the value of the variables in the parallelogram. /l

a. x = 13.5°, y = 56°, z = 153°b. x=4lo, y=27°,z= 112°c. x=27°, y=41°, 'z= 112°d. x = 56°, y = 13.5°, z = 153°

50. If ON =4x - 6, -LM =2x + 2, NM =X + 5, andOL =3y + 5, find the values of x and y given thatLMNO is a parallelogram.

a. x = 4;y=2

b. Ix = 8;y=2:

c. x = 8;y=2

d. I Ix = 4;y=2:

True or False:

51. If a quadrilateral is a parallelogram, thenconsecutive angles are equal in measure.

52. If a quadrilateral is a parallelogram, then oppositeangles are complementary.

8

62. Choose the statement that is NOT always true.For an isosceles trapezoida. the diagonals are congruent

53. AC a) 10 b)12 c) 8 d) 6 b. the base angles are congruentc. the diagonals are perpendiculard. the legs are congruent

54. BD a) 6 b)8 c) 10 d) 12

Use the diagram to find the given length.(ji'f1'. ==tI-'-===9i(

,\.

55. If the diagonals of a parallelogram areperpendicular, then the parallelogram is also whattype of figure? a) Rhombus '

b). Trapezoid ! c) Re:tangle I56. If the diagonals of a parallelogram are equal in

length, then the parallelogram IS also what type of

figure? a) Rectang~e; c) Rhombus \b) Trapezoid

57. Choose the statement that is NOT ALWAYS true.For a rhombus _a. each diagonal bisects a pair of opposite anglesb. all four sides are congruentc. the diagonals are congruentd. the diagonals are perpendicular

58. The diagonals of a parallelo gram always

a. are congruentb. are parallelc. bisect each otherd. are perpendicular

59. True or false: A rectangle is a parallelogram.

True or False:

60. All squares are parallelograms.

6l. Which statement is NOT always true of a rhombus?a. The diagonals are perpendicular to each other.b. The diagonals bisect each other.c. Each diagonal is longer than at least one side.d. The sum of the diagonals is less than the

perimeter.

63. For the trapezoid shown below, the measure of themidsegment is _

a. 29b. 58c. 25d. 30

9

64. Based on the markings, give the best name you can

• eo followingfigures.

<: ./ .J'....

b.V>

0c.

d. 065. Which type of quadrilateral has no parallel sides?

a. rectangleb. trapezoidc. rhombusd. kite

66. If all four sides of a quadrilateral are congruent, thequadrilateral is _a. a kiteb. a nonsquare rectanglec. a rhombusd. a trapezoid

67. Which of the following transformations representsan isometry?

xXpreimage image

a.

D [}prelIDage tmage

b.

9 (J)preimage image

c.

D DI

preimage image (

d.

68. The rule for this transformation of 6.ABC onto6.A'B'C'is ----

y,·········w. - - ..... - -.•..... !'1" •..... , ...•••••• t'"'f'~ ••• ..,•••••••• " •••••L.-. • ... 'A" .. ': : : : : .. B~ :C<r\: : : : ::::::::::: :::~B:::

-ic : : : : : : :: :::::::: :lO"'X

. • . . • . . '-.:1 El

a. (x, Y)4-(x - 9, Y - 2)b. (x,y) 4- (x + 9,y + 2)c. (x,Y)4-(x-9,y+2)d. (x,y)~(x+9,y-2)

10

69. A figure is translated using the vector (-2, 4). What a.translation vector would move the .image.back to itsoriginal position?

a) (2, -4 ) b) (-2, 4) c) ~2, 4 ) \

70. The translation vector is u=(-7, 4). If the image of

A is A' ( 6, - 4) ,·~~~_the coordinates ~f point A.

a) (1,0) b)(-l,O) c) (0,1) d) (13,-8)

71. The translation vector is u= (7, - 3). The image ofo point A is A' (5, -7). Find the coordinates of A.

a) (-2,4) b) (2,4)- c) (4, -2) d) ( 12, -10) b.

72. Use the graph below to complete the sentence.

-m : : : : : : ::

\ • - - .... 0-:16

Figure A' B' C'D' is the image of figure ABCDunder a rotation _a. 2700 clockwise about the origin.b. 1800 about the origin.c. 900 counterclockwise about the origin.d. 2700 counterclockwise about the origin.

73. True or False: The line is a line of symmetry for theshape below.

74. Which figure shows all lines of symmetry?

11

c.

d.

, 00

75. Which figure has more than 1 line of symmetry?

oa.

b.

c.

d.

76. Identify two chords.F__~~

a. DEandFG- -b. FGand HI

- -c. DFandEG- -d. DE and HI

77. A circle is the set of all points in a planethat

a. have a centerb. are equidistant from a given pointc. have a diameterd. lie within a given radius

12

78. The center of a circle lies on

a. every diameterb. the circlec. a tangent lined. every chord

79. If a circle has a diameter of 12, then it has __

a. a radius of4b. a radius of 24c. a radius of6d. a diameter of 6

80. Two coplanar circles are concentric if_. _.

a. they have the same centerb. they have exactly one point of intersectionc. they have no points of intersectiond. they have congruent radii

81. The circle is circumscribed by the pentagon asshown (not drawn to scale). If QZ = 8, IT = 7,XW = 12, UW = 14, and SU = 14, friicrtiie-perimeter of the pentagon.

Q

(,

S

T

y

x

v w

a. 82b. 117c. 89d. 110

82. You are standing at point B. Point B is 22 feet fromthe.center of the circular water storage tank and 20feet from point A. AB is tangent to 00 at A. Findthe radius of the tank.

a. 19.6 ft.b. 9.2 ft.c. 18.3 ft.d. 29.7 ft.

B

a

83. AB is tangent to 00 atA (not drawn to scale). Findthe length of the radius r, to the nearest tenth.

A 12

-84. Given: In 00, mBAC = 320°. Find mLA.

a. 20°b. 10°c. 13°d. 26°

A

85.

--a. EHF,.----.....b . FGH..--..c. EFG--d. FEH

86. Identify the minor congruent arcs in the figure.

D

13

)2....~-----G

.E

87. Find the value ofx.

a. 10.4b. 5.8c. 9.5d. - 7.1

---88. Given OQ and mLB = 55°, find mAC.

a. 55°b. 110°c. 125°d. 305°

Use the diagram (not drawn to scale) and the given /information. !

G--- --- ....-89. mBCD= 116°, mDEF=90°, mFGH= 138°, and..-mHAB= 16°FindmLFPD.

a. 24°b. 100°c. 16°d. 37°

...--... ---90. mAB = 85°, mCD = 25°

FindmLDOC.

a. 30°b. 55°c. 60°d. 110°

(I.

. Not drawn to scale

91. Find the measure of L1.

14

92. Find the measure of Ll.

Use the diagram (not drawn to scale) and the giveninformation.

A

o

B

. --..--93. Find the value ofx ifmAB = 410 and mCD = 38°.

94.

Find the value ofx.a. 21b. 12c. 8d. 14

15

95.

16x

24

Find the value 'of x.a. none of theseb. 2c. 8d. 3

96. Write the standard equation of a circle with itscenter at the origin and radius 7.

a. X2 +y2 = 49

b. X2 +y2 = 142 2

X Yc. 14 +14 = 1

d. X2 +y2 = 7

97. Write the standard equation of a circle with center(5, -1) and radius 2.

a. (x + 5) 2 - (y - 1f = 2

b. (x-5)2+(Y+l)2=4

c. (x + 5) 2 + (y - 1f = 2

d. (X-5)2 + (Y_l)2 =4

98. The standard equation of a circle with center (-4, 3)and radius 7 is --

a. (x _4)2 + (y + 3f = 7

b. (X-4)2+(Y+3f =49

c. (x+~l + (Y-3f = 49

d. (x + 4) + (y - 3) = 7

Find the area:

99.

IIIII

Ifi7 emI.IIII

L..- ...L r12.4 em

Given: ABeD is a parallelogram.

-', ~B _32------""117 Ci -A 10 E D

100. a. Find the height, BE.b. Find the area of MBE.

10 1. a. Find the height, BE.b. Find the area of parallel ogram ABCD.

102. The area of the parallelogram is __ .

a. 280 sq. unitsb .. 360 sq. unitsc. 600 sq. unitsd. 1110 sq. units

103. Find the area of the quadrilateral. (not drawn toscale)

/

(

a. 434b. 120c. 868d. 428

Find the area:

104.18 in.

30 in.

105. The area of a trapezoid is 218 in2. Ifthe height is 8in. and the longer base is 36 in., what is the lengthof the shorter base? Round your answer to thenearest tenth.a. 27.3 in.b. 6.1 in.c. 18.5 in.d. 8.8 in.

106. InrhombusABCD, AB= 15 andAC= 18. Find thearea of the rhombus to the nearest tenth.a. 21l.3b. 149.2c. 216.0d. 246.5

16

107. The figures are similar. Find the missing values.

p=?

12

A=72D34

109. Find the circumference of a circle with radius 5 ID.

Use Jr::::3.14. a) 62.8 b) 31.4 c)78.S \

110. A circle has a circumference of 40 meters. Find itsradius.a. 20mb. 6.37mc. 10md. 12.73 m 113.

108. The ratio of the side lengths of two regularhexagons is 3 to 8. If the area of the smallerhexagon is 18 square units, then the area of the .larger hexagon is __ .

a. 24 sq. unitsb. 48 sq. unitsc. 128 sq. units

d.64 ."9 sq. units •

17

111. An expression for the circumference of a circlewith diameter d is

Jrd2

a. 4b. Jrrc. Jrdd. 2Jrd

112. .Find the length of a 60° arc in a circle with a radiusof4.

8Jr9

b. 8Jr8Jr3

4Jrd. 9

a.

c.

Find the area:

a. 153.86 m2b. 38.465 m2c. 9.61625 m2d. 21.98 m2

114. Find the area of the shaded sector in terms of Jr.

Find the area of the shaded sector to the nearestwhole number.

115.

119. Find the surface area of the triangular prism.

~;

;;

;~~~~";;

;,~of..,..,&.---------~•.•...... ~

11 em

(

117. Find the area of an equilateral triangle with sidelength 6.a. 36b. 9~c. 9~d. 18

118. Find the area of a regular pentagon with radius 5em. Round to the nearest tenth.a. 36.7 em"b. 59.4 crrr'c. 118.9 ern"d. 78.0 cm2

a. 2658.6 em-b. 1994.0 em-

c. 1329.3 em-d. 271,814.4 ern?

18

/ . 7••I

13 in. I,1- ________

J /I(l,In.

2Sin.a. 336 ft2

a. 1548 :in.2 b. 532 ft2b. 1794 :in.2 168 ft2c.

( 2388 :in.2 84 ft2c. d.\.

d. 2664:in.2

(120. Find the surface area of the right prism below.

121. If all the angles in the faces of the polyhedronbelow are right angles, then its surface area is

122. Find the surface area of the cylinder to the nearestsquare unit. Use n ~ 3.14.

5.3m

a. 25 m2b. 156 m2c. 78 m2d. 16 m2

123. Find the surface area of the right cylinder below.(Round the result to two decimal places.)

124. Find the surface area of the lateral faces on theregular pyramid below.

19

125. The pyramid shown has a rectangular base andfaces that are isosceles triangles. Find the totalsurface area to the nearest tenth.

2ft

a. 20.0 feb. 52.0 ft2c. 45.8 ft2d. 39.2 ft2

126. The surface area of the right cone shown is .

a. 447l' in. 2

b. 1127l' in. 2

c. 1653 7l' in. 2

d. 367l' in. 2

127. An aquarium in a restaurant is a rectangular prismand measures 3.5 feet by 4 feet by 3 feet. What isthe volume of the aquarium?

a. 36 cubic feetb. 15.5 cubic feetc. 10.5 cubic feetd. 42 cubic feet

20

128. Find the volume of the right triangular prism.

8m

a. 60m3

b. 288m3

c. 576m3

d. 36m3

129. Find the volume of the right prism.

130. The pyramid shown has a rectangular base andfaces that are isosceles triangles. Find its volume.

6ft

( 131. Calculate the volume of the cone. Use Jrr::J 3.14.

a. 12m3

b. 113.04 m3

9.42m 3c.d. 37.68 m 3

a) 5 b) 10

132. Find the diameter of a sphere that has a surface areaof 100Jr in2.

(

c) 100 d) 25 \

133. Find the surface area of a sphere that has a diameterof 20 em.Express your answer in terms of Jr.

a. 25Jr em'b. 400Jr em'

500 3c. 3Jrcm

d. 100Jr cm2

134. Find the volume of a sphere 16 ft in diameter. Use;r r::J 3.14 and round your answer to the nearesttenth.a. 1205.8 ft3b. 2143.6 ft3c. 267.9 ft3d. 301.4 fe

21

135. The top of the cylindrical container shown has theshape of a hemisphere. The total volume of thecontainer is --

r=:3 in.

a. 36;r in. 3

b. 72;r . 3m.

c. 72 in. 3

d. 144Jr . 3m,