GEOMETRY 2014-2015 SEMESTER EXAMS PRACTICE MATERIALS ... · GEOMETRY 2014-2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 2014-2015 Page 1 of 37 Revised October 2014 Clark County

GEOMETRY 2014-2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1

2014-2015 Page 1 of 37 Revised October 2014 Clark County School District

1. (2.1-1) A figure is transformed in the plane such that no point maps to itself. What type of transformation must this be?

(A) dilation

(B) reflection

(C) rotation

(D) translation

For question 2, determine the truth of the statements about rotations.

2. (2.1-2) Under a rotation, no point can map to itself.

(A) True

(B) False

3. (2.2-1) What term describes a transformation that does not change a figure’s size or shape?

(A) similarity

(B) isometry

(C) collinearity

(D) symmetry

For questions 4-7, determine if the described transformation(s) is/are an isometry.

4. (2.2-2) A reflection is an isometry.

(A) True

(B) False

5. (2.2-3) A composition of two reflections is an isometry.

(A) True

(B) False

6. (2.2-4) A dilation is an isometry.

(A) True

(B) False



7. (2.2-5) A composition of a rotation and a dilation is an isometry.

(A) True

(B) False

For question 8, a transformation S is defined as , 3 , 1x y x y .

8. (2.2-6) S is an isometry.

(A) True

(B) False

For questions 9-12, determine if the mapping is an isometry.

9. (2.2-7) , , 2x y x y is an isometry.

(A) True

(B) False

10. (2.2-8) , ,x y x y is an isometry.

(A) True

(B) False

11. (2.2-9) , ,x y y x is an isometry.

(A) True

(B) False

12. (2.2-10) , 2 ,x y x y is an isometry.

(A) True

(B) False



13. (2.3-1) Use the figure.

A transformation T is defined as , , –x y x y .

Which shows the image of figure under T?

(A)

(B)

(C)

x

y

x

y

x

y

x

y



14. (2.3-2) Which transformation does NOT preserve the orientation of a figure?

(A) dilation

(B) reflection

(C) rotation

(D) translation

For question 15, determine the truth of the statements about rotations.

15. (2.3-3) Rotations preserve the orientation of a figure.

(A) True

(B) False

For question 16-17, point P is located at (6, 0) and undergoes a transformation.

16. (2.3-4) A rotation of 90° about P results in P = P.

(A) True

(B) False

17. (2.3-5) A translation by the vector 6, 0 results in P = P.

(A) True

(B) False

18. (2.3-6) Use the figure.

(a) Transform ABC by reflecting it across the y-axis to produce A B C .

(b) Describe a transformation, or composition of transformations, that maps A B C to DEF .

(c) Describe a single transformation that maps ABC to DEF .

A

CB

D

EF

x

y



19. ( 2.3-7) A B C is the image of ABC when a

reflected about line .

Construct line �

20. (2.4-1) What is the image of the point (–4, 6) under the transformation

, ,T x y y x ?

(A) (6, 4)

(B) (–6, –4)

(C) (4, 6)

(D) (–4, –6)

21. (2.4-2) A figure is rotated about the origin by 180°, then is translated 4 units right and one unit up. Which describes the results of the two transformations?

(A) , 4, 1x y x y

(B) , 4, 1x y x y

(C) , 4, 1x y y x

(D) , 4, 1x y y x

For question 22, a transformation S is defined as , 3 , 1x y x y .

22. (2.4-3) The pre-image of 3, 6A under S is 9, 5A .

(A) True

(B) False

A B'

C'

A'

B

C



23. (2.4-4) Given point A is located at (1, 3). What is the final image of A after this series of transformations?

(1) Reflect A across the y axis. (2) Translate the image such that , 4, 2x y x y .

(A) (–1, –3)

(B) (–3, 5)

(C) (–3, –1)

(D) (–5, 5)

24. (2.4-5) A reflection about the x axis results in P = P.

(A) True

(B) False

25. (2.5-1) The point A(4, 3) is rotated –90° about the origin. In which quadrant is A' ?

(A) I

(B) II

(C) III

(D) IV

26. (2.5-2) Use the diagram.

Which series of reflections would result in a rotation of –44° about A?

(A) reflect across k¸ then reflect across

(B) reflect across ¸ then reflect across k

(C) reflect across ¸ then reflect across m

(D) reflect across m¸ then reflect across

k

A

m

44° 22°



27. (2.5-3) After a figure is rotated, P P . Which statement(s) could be true?

(A) The center of rotation is P.

(B) The angle of rotation is a multiple of 360°.

(C) Either A or B or both.

(D) Neither A nor B.

28. (2.5-4) Draw the image of ABC when rotated 70° about O.

29. (2.5-5) A B C is the image of ABC when rotated about point O. Construct point O and compute the angle of rotation.

A

B

C

O



30. (2.6-1) Which of these is equivalent to a translation?

(A) a reflection across one line

(B) a composition of two reflections across intersecting lines

(C) a composition of two reflections across parallel lines

31. (2.6-2) In the diagram, g h and B lies on line g.

A

B'

C'

A'

B

C

g h

A

B C5cm

10cm



The figure ABC is reflected across line g, and its image is reflected across line h. What is the distance from line g to the final image of point A?

(A) 5 cm

(B) 15 cm

(C) 20 cm

(D) 25 cm

32. (2.6-3) A figure is reflected across the line y = 2, then reflected across the line y = 4. Which single transformation results in the same image?

(A) a reflection across the line y = 3

(B) a reflection across the line y = 6

(C) a translation 2 units up

(D) a translation 4 units up

33. (2.6-4) Point A is the image of point A under a transformation T. Line is the

perpendicular bisector of AA at point M. Which describes the transformation T?

(A) a reflection across

(B) a 90° rotation about M

(C) a translation by the vector from A to M

(D) a dilation about M with scale factor 2

Forquestions34‐35,usethediagramwhichshowsABChasbeenreflectedacrossanunknownline,thenreflectedacrosslinemtoproduceABC.



34. (2.6-5) The equation of line is x = –0.5.

(A) True

(B) False

35. (2.6-6) If ABC were reflected across line m first, then reflected across line to

produce ABC, the equation of line would be x = –0.5.

(A) True

(B) False

36.(2.6‐7)Jimmyisbuildingago‐carttorace.Jimmysitsinaseattowardtheleftrearcornerofthecart.Toseeothercartsbehindhim,hemounts3planemirrors:oneoneachsideofthecartandoneinthecenter.

The scale diagram shows a top view of the cart.

x

y

C A

B

CA

Bm



(a) Jimmy’s eyes are at point J. The mirrors are mounted in a way that Jimmy does not block his own view. Show the area behind the cart that Jimmy can see using the mirrors.

(b) Describe how Jimmy could improve his visibility behind the cart using the same three mirrors.

37. (2.6-8) Draw the image of ABC when reflected across line m.

For questions 38-40, use the diagram showing parallelogram ABCD.

J

centermirror

leftsidemirror rightsidemirror

FrontofCart

Seat

1foot

A

B

C

m



38. (2.8-1) A reflection across carries parallelogram ABCD onto itself.

(A) True

(B) False

39. (2.8-2) A rotation of 90° about I carries parallelogram ABCD onto itself.

(A) True

(B) False

40. (2.8-3) A rotation of 180° about I carries parallelogram ABCD onto itself.

(A) True

(B) False

41. (2.8-4) A regular polygon with n sides is carried onto itself by a positive rotation about its center that is a multiple of 60°, but less than 360°.

Which could NOT be the value of n?

(A) 3

(B) 4

(C) 5

(D) 6

42. (3.1-1) Look at the figure below.

A

CD

H

G

E

FI

EG



Look at these three figures.

Which figures are congruent to the first figure?

(A) I only

(B) II only

(C) I and II only

(D) I, II, and III

For questions 43-45, evaluate whether the image of a figure under the described transformation is congruent to the figure.

43. (3.2-1) A transformation T follows the rule , 3,x y x y . The image of a

figure under T is congruent to the figure.

(A) True

(B) False

44. (3.2-2) A transformation T follows the rule , ,x y y x . The image of a

figure under T is congruent to the figure.

(A) True

(B) False

45. (3.2-3) A transformation T follows the rule , , 2x y x y . The image of a figure

under T is congruent to the figure.

I

II

III



(A) True

(B) False

46. (3.2-4) The diagram shows regular hexagon ABCDEF with center O.

For each part, fill in the blank.

(a) _____ is the image of A under a 60° rotation about O.

(b) The figure is reflected across . The pre-image of E is _____.

(c) F is the image of D when the figure is rotated _____° about O.

(d) B is first reflected across . That image maps to F when reflected across _____.

47. (3.3-1) On the coordinate plane, draw triangles ABC and ABC such that:

(1) A = A

(2) ABC has been rotated 90°.

Forquestions48‐50,consideratriangle ABC thathasbeentransformedthroughrigidmotionsanditsimagecomparedto XYZ .Determineifthegiveninformationissufficienttodrawtheprovidedconclusion.

48.(3.4-1)

Given Conclusion

A X

B Y

C Z

ABC XYZ

(A) True

(B) False

49. (3.4-2)

FC

AD

A

B

C D

EO

F



Given Conclusion

A X

B Y

BC YZ

ABC XYZ

(A) True

(B) False

50. (3.4-3)

Given Conclusion A X

AB XY

BC YZ

ABC XYZ

(A) True

(B) False

51. (3.4-4) In the diagram, m is the perpendicular bisector of AB at C, and mr D E .

Prove ADC BEC .

52. (3.4-5) In the diagram, is the perpendicular bisector of AB . DC

A BC

D E

m



Prove DAB DBA .


Given: BD AC AE BC

Prove: AEC BDC


Which statement would be used to prove lines r and s are parallel?

(A) 1 and 3 are congruent

(B) 2 and 7 are complementary

(C) 4 and 1 are congruent

(D) 8 and 6 are supplementary

55. (3.5-2) In the diagram, m n and p q .

A

BC

D

F

CD

A

E

B

sr

1

5

2 3 4

678

m

n

m

p

88°n

x°

q



What is the value of x?

(A) 44

(B) 88

(C) 92

(D) 176

For questions 56-59, use the diagram where B is the reflection of A across .

56. (3.6-1) PA = PB

(A) True

(B) False

57. (3.6-2) AB

(A) True

(B) False

58. (3.6-3) AQ = QB

(A) True

(B) False

59. (3.6-4) 1

2PQ AB

(A) True

(B) False

60. (4.1-1) In ABC , M is the midpoint of AB and N is the midpoint of AC . For which

type of triangle is 1

2MN BC ?

(A) equilateral only

(B) isosceles only

(C) scalene only

(D) any triangle

For questions 61-62, consider ABC where AB = BC and 40m A .

PQ

PQ

A B

P

Q



61. (4.2-1) 140m B m C

(A) True

(B) False

62. (4.2-2) 100m C

(A) True

(B) False

63. (4.2-3) Prove the sum of the measures of the interior angles of any triangle is 180°.

For questions 64-66, use the diagram where ABCD is a quadrilateral with AB CD and

AD BC . Diagonals AC and BD intersect at E.

64. (4.3-1) CBE ABE

(A) True

(B) False

65. (4.3-2) ADE ABE

(A) True

(B) False

66. (4.3-3) CDE ABE

(A) True

(B) False

67. (4.4-1) Use scalene right triangle ABC.

DC

AB

E

A

B

C



Describe and sketch the transformations required so that the union of the triangle and its image forms

(a) a kite.

(b) an isosceles triangle.

(c) a rectangle.

68. (4.6-1) Use the Venn diagram.

A quadrilateral ABCD has 4 lines of symmetry. Identify the area of the diagram in which ABCD resides.

(A) III

(B) IV

(C) V

(D) VII

69. (5.1-1) Triangle ABC has vertices 2, 2A , 5, 5B , and 5, 3C . The triangle

is dilated about the point 1, 1 with scale factor 4. What is the location of A' ?

(A) 8, 8

(B) 10, 10

(C) 11, 5

(D) 14, 6

Trapezoids Kites

QuadrilateralI

VI VII

SquaresRhombi Rectangles

III IV V

ParallelogramII




Dilate line m about the origin with scale factor 2. What is the equation of the line’s image?

(A) y = 2x + 2

(B) y = 2x + 4

(C) y = 4x + 2

(D) y = 4x +

x

y

m




Dilate line m by a factor 1

2 about P. Which shows the result of the dilation?

(A)

(B)

(C)

(D)

m

x

y

P

m'

x

y

P

m'

x

y

P

m'

x

y

P

m'

x

y

P



72. (5.1-4) In the diagram, segments AB and CD intersect at E, F lies on AB , and 60m AEC .

The two segments are dilated about F with scale

factor 1

2. What is m A E C ?

(A) 30°

(B) 60°

(C) 90°

(D) 120°

For questions 73-75, use the diagram.

Let the figure be dilated with scale factor k, where k 0 and k 1.

73. (5.1-5) m A B E k m ABE .

(A) True

(B) False

74. (5.1-6) G' is between B' and F'.

(A) True

(B) False

E

B

AF

G

F

D

C

A

60°

C

D B

FE



75. (5.1-7) C D k CD

(A) True

(B) False

76. (5.1-8) Use the figure below.

Which shows the figure dilated about the origin with scale factor 1.5?

(A)

(B)

(C)

x

y

x

y

x

y

x

y



77. (5.1-9) One vertex of a polygon is A(–4, 5). If the polygon is dilated about the point (0, 2) with scale factor –2, what is the location of A?

(A) (–8, 8)

(B) (–8, 10)

(C) (8, –10)

(D) (8, –4)

78. (5.2-1) In the diagram, ABCD is dilated with center O to produce A'B'C'D', and 1

3A B AB .

What is OA

AA

?

(A) 1

3

(B) 1

2

(C) 2

(D) 3

79. (5.2-2) J(5, 7) is the image of J(3, 3) after a dilation with scale factor 3. Where is the center of dilation?

(A) (–3, –9)

(B) (0, 0)

(C) (2, 1)

(D) (4, 5)

A

B'

A'

B

C'

D

C

D'O



80. (5.2-3) In the diagram, A B C is a dilation of ABC .

(a) Find the center of dilation O.

(b) Compute the scale factor of the dilation.

81. (5.9-1) Right triangle PQR has sides of length 6 units, 8 units, and 10 units. The triangle is dilated by a scale factor of 4 about point Q. What is the area of triangle P'Q'R'?

(A) 96 square units

(B) 192 square units

(C) 384 square units

(D) 768 square units

82. (5.10-1) In the diagram below BC DH .

What is the value of y?

(A) 13

(B) 18

(C) 27

C'

A'

B' C

A

B

A

4

B C

D H

8

9

y



83. (5.10-2) The ratio of the side lengths of a triangle is 3:6:8. A second triangle is similar to the first and its shortest side measures 8.0 centimeters. What is the length of the longest side of the second triangle?

(A) 3.0 cm

(B) 10.7 cm

(C) 13.0 cm

(D) 21.3 cm

84. (5.11H-1) (HONORS) Triangle ABC has sides of length 3, 6, and 8. Triangle DEF is similar to triangle ABC and has one side with length 24.

(a) What are the possible scale factors of the dilation of triangle ABC to triangle DEF?

(b) Compute one possible area of triangle DEF.

85. (5.12-1) In the diagram, a student has placed a mirror on level ground, then stands so that the top of a nearby tree is visible in the mirror.

What is the height of the tree?

(A) 24 m

(B) 35 m

(C) 41 m

(D) 59 m

86. (5.12-2) In the diagram, JG QR .

What is the value of x?

(A) 11

(B) 6

(C) 5

(D) 3

R

J

P

G

Q

8x

74

2m

36m3m



87. (5.12-3) Triangle One has vertices (2, 4), (2, 8), and (5, 4). Triangle Two is similar to Triangle One and has two of its vertices at (–1, 1) and (–7, 1).

(a) Draw Triangle One and Triangle Two on the coordinate plane and label the vertices.

(b) Draw and label a third triangle that is similar to Triangle One, has two vertices at (–1, 1) and (–7, 1), but is not congruent to Triangle Two.

88. (5.13-1) Which figure contains two similar triangles that are NOT congruent?

(A)

(B)

(C)

(D)

89. (5.13-2) Which is NOT a criterion for triangle similarity?

(A) angle-angle

(B) angle-side-angle

(C) side-angle-side

(D) side-side



90. (5.14-1) Sally constructs a triangle where two of the angles measure 50° and 60°. Tom constructs a triangle where two of the angles measure 50° and 70°. What is true about the two triangles?

(A) The triangles cannot be similar.

(B) The triangles could be similar.

(C) The triangles must be similar.

91. (5.14-2) Prove that any two isosceles right triangles are similar.


Which is equal to h?

(A) ay

(B) bx

(C) xy

(D) ab

93. (6.1-2) In the diagram, ABC is a right triangle with right angle C, and CD is an altitude of ABC .

Use the fact that ABC ACD CBD to

prove 2 2 2a b c .

C

A BD

c

bh

x y

a

C

A BD

c

b a

d e



94. (6.4-1) In GHI , the sine of angle G equals 1

2. G H I is a dilation of GHI

about G with a scale factor of 2. What is the sine of angle G' ?

(A) 1

4

(B) 1

2

(C) 3

2

(D) 1

95. (6.5-1) Let cos A m . What is the value of sin A?

(A) m

(B) 1 – m

(C) 21 m

(D) 1 m


Which statement is true?

(A) 13

sin5

A

(B) 12

cos13

A

(C) 12

tan5

A

97. (6.5-3) In the diagram, BC < BD and BD = AD.

Which statement is true?

(A) cos sinABC DAB

(B) cos sinABC DAB

(C) cos sinABC DAB

C A

B

12

135

C

A B

D



98. (6.6-1) What is 1 3cos

2

?

(A) 30°

(B) 45°

(C) 60°

(D) 90°

99. (6.6-2) What is tan 60°?

(A) 2

2

(B) 3

2

(C) 1

3

(D) 3

100. (6.6-3) What is 1tan 1 ?

(A) 30°

(B) 45°

(C) 60°

(D) 90°

For question 101, use the following statement. Given: An angle measures k°, where k > 0.

101. (6.7-1) sin cos 90k k

(A) True

(B) False

102. (6.7-2) In ABC where C is a right angle, 7

sin4

A . What is cos B?



(A) 7

4

(B) 7

3

(C) 3

4

(D) 3

7

For questions 103-104, let cos x m .

103. (6.7-3) cos 90 x = m

(A) True

(B) False

104. (6.7-4) sin 90 x = m

(A) True

(B) False

105. (6.7-5) Let cos28a . Which statement is true?

(A) cos 62a

(B) cos 152a

(C) sin 62a

(D) sin 152a




Which is the value of x?

(A) 41cos35x

(B) tan35

41x

(C) 41

cos35x

(D) 41

tan35x


What is the value of d ?

(A) 5

(B) 5 2

(C) 10

(D) 10 2

108. (6.10-1) Fred stands at corner A of a rectangular field shown below. He needs to get to corner C.

What is the shortest distance from A to C?

(A) 9 m

(B) 13 m

(C) 15 m

(D) 21 m

35°A

B

Cx

41

d

45°

12m

9m

D C

BA



109. (6.10-2) Use the right triangle. What is the value of x?

(A) 7

(B) 161

(C) 7

(D) 17

110. (6.10-3) The diagram shows a model of a closet floor on which Kim is laying carpet. (Measurements are approximate.)

(a) What is the area of the closet?

(b) The carpet Kim is using is cut by the carpet store in rectangular pieces from a 4-foot wide roll. What is the shortest length of carpet Kim would need to cover the closet floor in a single piece? Justify your answer.

15x

8

13

23

36

29

2

145°

145°



111. (6.15H-1) (HONORS) Consider a triangle ABC. Which statement is true?

(A) 2 2 2 2 cosc a b ab C

(B) 2 2 2 2 cosc a b ab C

(C) 2 2 2 2 cosc a b ab C

(D) 2 2 2 2 cosc a b ab C

112. (6.15H-2) (HONORS) Use the diagram.

What is cos A?

(A) 16

56

(B) 56

16

(C) 16

56

(D) 56

16

113. (6.16H-1) (HONORS) The diagram shows a surveyor’s map.

The surveyor is trying to measure the direct distance between points A and B, which are on opposite sides of a lake. From point C, point A is 950 meters away in a direction 20° west of north. From point C, point B is 880 meters away in a direction 50° east of north.

Which represents the distance between A and B?

(A) 2 2950 880 2 950 880 cos70

(B) 880 950

sin50 sin 20

(C) 950 sin70

sin55

A

B C9

4 7

C

A

B

20°950m 50°880m



114. (6.16H-2) (HONORS) A small airplane flies due north at 150 kilometers per hour. A wind is blowing towards the direction 60° east of north at 50 kilometers per hour. Which figure represents the final speed and direction of the airplane?

(A)

(B)

(C)

(D)

For questions 115-117, consider a triangle ABC and each given set of measurements.

115. (6.16H-3) (HONORS) AB, AC, and m A are sufficient to solve the triangle using the Law of Sines.

(A) True

(B) False

116. (6.16H-4) (HONORS) AB, AC, and m B are sufficient to solve the triangle using the Law of Sines.

(A) True

(B) False

117. (6.16H-5) (HONORS) AB, AC, and BC are sufficient to solve the triangle using the Law of Sines.

(A) True

(B) False

N

N

N

N



118. (6.16H-6) (HONORS) Given: cos26 0.90 and sin26 0.44

What is the approximate value of cos 154?

(A) –0.90

(B) –0.44

(C) 0.44

(D) 0.90

For questions 119-120 use the statement below.

Given: An angle measures k°, where k > 0.

119. (6.16H-7) (HONORS) sin sin 180k k

(A) True

(B) False

120. (6.16H-8) (HONORS) cos cos 180k k

(A) True

(B) False

For question 121, let cos x m .

121. (6.16H-9) (HONORS) cos 180 x = m

(A) True

(B) False

122. (6.16H-10) (HONORS) In triangle ABC, 25m B , a = 6.2, and b = 4. Find all possible measures of the remaining two angles and the third side.

123. (6.16H-11) (HONORS) In triangle ABC, 25m B , a = 6.2, and c = 4.

(a) Find all possible measures of the remaining two angles and the third side.

(b) Findallpossibleareasofthetriangle



124. (6.18H-1) (HONORS) The diagram shows a parallelogram ABCD.

What is the parallelogram’s area?

(A) 7.5 3

(B) 15

(C) 15 3

(D) 30 3

125. (6.18H-2) (HONORS) In the diagram, ABC is a non-right triangle.

Which describes the area of the triangle?

(A) 1

2ab

(B) sinab C

(C) 1

sin2

ab C

(D) 1

cos2

ab C

C

A

B

D

5

60°3

C

B Ac

a b

Documents

GEOMETRY 2014-2015 SEMESTER EXAMS PRACTICE MATERIALS ... · GEOMETRY 2014-2015 SEMESTER EXAMS PRACTICE MATERIALS SEMESTER 1 2014-2015 Page 1 of 37 Revised October 2014 Clark County