Geometry Regents Review Name: DateGiven: AB = BC Dis the midpoint of AB Eis the midpoint of CB Prove: AE = DC statement reason 1. AB = BC given 2. DB = 1 2 (AB) defn. of midpoint 3

Geometry Regents Review

Name: Date:

1. A set of points that extend indefinitely in twoopposite directions is called .

A. a line B. an angle

C. a plane D. a ray

2. Two non-parallel lines intersect at a .

A. point B. line C. plane

D. none of these

3. Which of the following sets of points are collinear?

A. A, B, D

B. A, B, C

C. B, D, C

D. C, A, D

4. What is the image of point A after a rotation of90◦ in the clockwise direction?

�

��

�

•A

•B

C•

D•

•E

•H

G•

F•

A. C B. D C. E D. F

5. What is the image of (5, 1) under acounterclockwise rotation of 90◦ ?

A. (1, 5) B. (−1, 5)

C. (−1,−5) D. (0, 0)

6. Find the coordinates of P′, the image of P(−2, 1)after a clockwise rotation of 180◦ about the origin.

A. (2,−1) B. (2, 1)

C. (−1, 2) D. (1,−2)

7. Select the letters that would appear the same aftera 180◦ rotation about the center.

I. A

II. H

III. R

IV. S

A. I only B. II only

C. III only D. II and IV

page 1

8. A′ is the image of A. Which of the followingrotations could be used to perform thistransformation?

I. 90◦ clockwise

II. 90◦ counterclockwise

III. 270◦ clockwise

IV. 270◦ counterclockwise

�

��

�

•A

•A′

A. II only B. II and III

C. III only D. II and IV

9. A point (3, 5) is reflected over the x-axis. Whatare the coordinates of the image point?

A. (3, 0) B. (3,−5)

C. (−5, 3) D. (−3, 5)

10. Find Q′, the image of Q(2,−3), after a reflectionacross the line y = x.

A. (−2,−3) B. (−2, 3)

C. (−3, 2) D. (3,−2)

11. What is the the rotational symmetry of a rhombus?

A. 120◦ B. 100◦ C. 90◦ D. 60◦

12. In the diagram, K and K′ are congruent.

Which of the following is a way of transformingK into K′ ?

A. a rotation of 180◦ about the origin

B. a clockwise rotation of 90◦ about the point(0, 2)

C. a reflection across the x-axis, then atranslation down 2 units

D. a reflection across the y-axis, then a reflectionacross the line y = 2

13. Which of the following is not a congruencetransformation for a two-dimensional figure?

A. dilation B. rotation

C. reflection D. translation

14. State the congruence relation for ^XYZ and^PQR.

A. ASA

B. AAA

C. SAS

D. not necessarilycongruent

page 2 Geometry Regents Review

15. State the congruence relation for ÂBC and^DEF.

A. SSS

B. SSA

C. ASA

D. SAS

16. The ASA congruency axiom states that twotriangles are congruent if:

A. two angles and the contained side of onetriangle are equal to two angles and thecontained angle of the other triangle.

B. two sides and the contained angle of onetriangle are equal to two sides and thecontained angle of the other triangle.

C. two angles and a side of one triangle areequal to two angles and a side of the othertriangle.

D. two sides and the excluded angle of onetriangle are equal to two sides and theexcluded angle of the other triangle.

17. The Corresponding Angles Conjecture states thatif two parallel lines are cut by a transversal, thecorresponding angles are congruent. The picturebelow shows this relationship.

Which of these congruent angles are correspondingangles?

A. ∠1 and ∠4 B. ∠1 and ∠3

C. ∠4 and ∠8 D. ∠4 and ∠3

18. The perpendicular bisector of a line segment willresult in angles that are .

A. acute B. obtuse

C. right D. complementary


19.

In hexagon DRAGON the diagonals−−−RO and

−−−AN bisect each other. Jared’s geometry class is writing a proof to

show that−−−RA ∼=

−−−−ON.

Statement Reason

1.−−−RO bisects

−−−AN,

−−−AN bisects

−−−RO 1. given

2.−−−RS ∼=

−−−SO,−−−AS ∼=

−−−SN 2. Definition of segment bisector

3. ∠OSN ∼= ∠ASR 3.

4. ^NOS ∼= ÂRS 4. SAS

5.−−−RA ∼=

−−−−ON 5. CPCTC

The teacher asks Jared to justify step three. What should he answer?

A. Adjacent angles are congruent. B. Vertical angles are congruent.

C. Alternate Interior angles are congruent. D. Definition of angle bisector.

20. Given:−−−AB ∼=

−−−AC

Prove: ∠3 ∼= ∠4

statement reason

1.−−−AB ∼=

−−−AC 1.


21. Given: LF = KF

LA = KA

Prove: LJ = KJ

statement reason

22. Given:−−−−WY is the angle bisector of ∠XWZ

m∠XYW = m∠ZYW

Prove: ^WXY ∼= ^WZY

statement reason−−−−WY is the ∠ bisector of ∠XWZ (1)

m∠XWY = m∠ZWY (2)

WY = WY (3)

m∠XYW = m∠ZYW (4)

^WXY ∼= ^WZY (5)

In the above proof, what is reason (3)?

A. definition of an altitude

B. sides opposite equal ∠s are equal

C. reflexive property

D. definition of a right angle

23. Given:−−−−WY is the angle bisector of ∠XWZ

m∠XYW = m∠ZYW

Prove: ^WXY ∼= ^WZY

statement reason−−−−WY is the ∠ bisector of ∠XWZ (1)

m∠XWY = m∠ZWY (2)

WY = WY (3)

m∠XYW = m∠ZYW (4)

^WXY ∼= ^WZY (5)


A. given

B. definition of an altitude

C. definition of angle bisector

D. definition of a perpendicular


24. Given:−−−VX is a median of ^VWY

WZ = YZ

Prove: ^WXZ ∼= ^YXZ

Statement Reason−−−VX is a median of ^VWY (1)

X is the midpoint of−−−−WY (2)

WX = YX (3)

XZ = XZ (4)

WZ = YZ (5)

^WXZ ∼= ^YXZ (6)


A. definition of median

B. definition of midpoint

C. definition of perpendicular bisector

D. given

25. Given:−−−VT bisects

−−−−RW

−−−−RW bisects

−−−TV

Prove: ^RSV ∼= ^WST

Statement Reason−−−VT bisects

−−−−RW (1)

RS = WS (2)

m∠RSV = m∠WST (3)−−−−RW bisects

−−−TV (4)

TS = VS (5)

^RSV ∼= ^WST (6)

In the proof, what is the reason for (6)?

A. AAA B. ASA C. SAS D. SSS


26. Given:−−−AB ‖

−−−−DC

AB = DC

Prove: m∠DAC = m∠BCA

Statement Reason−−−AB ‖

−−−−DC (1)

AB = DC (2)

m∠BAC = m∠DCA (3)

AC = AC (4)

ÂDC ∼= ^CBA (5)

m∠DAC = m∠BCA (6)


A. CPCTC

B. SSS

C. vertical angles

D. alternate interior angles

27. Given:−−−AC is the median to

−−−BE

−−−EC is the median to

−−−AD

Prove:−−−AB ‖

−−−ED

statement reason

1.−−−AC is the median to

−−−BE

2. BC = CE

3. m∠1 = m∠2

4.−−−EC is the median to

−−−AD

5. AC = CD

6. ÂCB ∼= ^DCE

7. m∠3 = m∠4

8.−−−AB ‖

−−−ED

In the proof, what is the reason for line 7?

A. alternate interior angles are congruent

B. definition of parallel

C. isosceles triangle theorem

D. CPCTC

28. In the proof, what is the reason for line 3?

A. alternate interior angles are congruent

B. vertical angles are congruent

C. corresponding angles are congruent

D. definition of a median


29. Given:−−−AD is the perpendicular bisector of

−−−BC

Prove: ÂBC is isosceles

Statement Reason

1.−−−AD is ⊥ bisector of

−−−BC given

2. def’n of ⊥ bisector

3. def’n of ⊥ bisector

4.−−−AD ∼=

−−−AD

5. ÂBD ∼= ÂCD SAS

6. AB = AC

7. ÂBC is isosceles

What is the reason for step 7?

A. m∠B = m∠C

B. definition of isosceles (AB = AC)

C. angles opposite = sides are =

D. sides opposite = angles are =

30. Hazel says, “All isosceles triangles are congruent.”Amir says, “All isosceles triangles are similar.”Who is correct? Explain your reasoning.


31. Complete the following proof.

Given: AB = BC

D is the midpoint of−−−AB

E is the midpoint of−−−CB

Prove: AE = DC

statement reason

1. AB = BC given

2. DB = 12 (AB) defn. of midpoint

3. BE = 12 (BC) defn. of midpoint

4. both 12 of equal lengths

5. m∠B = m∠B

6.

7. AE = DC

32. Fill in the missing statements and reasons for the following proof.

Given:−−−AC ∼=

−−−BC

−−−−CM is the angle bisector of ∠C

Prove: ∠1 ∼= ∠2

statement reason

1. given

2. ∠ACP ∼= ∠BCP

3.−−−CP ∼=

−−−CP reflective property

4.

5. ∠1 ∼= ∠2


33. Given:−−−AE ⊥

−−−DB

−−−CF ⊥

−−−DB

m∠BAE = m∠DCF


−−−−DC

Statements Reasons

34. Given: m∠BAC = m∠BCA

AD = DC

Prove:−−−BD bisects ∠ABC

Statements Reasons


35. Given: BA = BC,−−−BD bisects ∠ABC

Prove: m∠BDC = 90◦

Statements Reasons

36. Given:−−−BE is the perpendicular bisector of

−−−AC,

m∠FBE = m∠DBE, FB = DB

Prove: AF = CD

Statements Reasons


37. Given: AB = AC, m∠1 = m∠2

Prove: DB = EC

Statements Reasons

38. Given: m∠CAB = m∠CBA

AM = BN

Prove: BM = AN

Statements Reasons


39. Given:−−−AC is the median to

−−−BE,

−−−EC is the median to

−−−AD.


−−−ED

Statements Reasons

40. Given: ÂBC is equilateral,^DEF is equilateral.

Prove: ÂFD ∼= ^BDE

Statements Reasons

41. RHOM is a rhombus. A, B, C, and D are themidpoints of each side. Prove that ABCD is arectangle.

42. In the figure,−−−TU ‖

−−−QR. Which proportion is not

true?

A.QRRS

=TUUS

B.QRQS

=TUTS

C.RUQR

=USTU

D.STTU

=SQQR


43. How many similar triangles are in the diagram?

A. 1 B. 2 C. 3

D. cannot be determined

44. In the diagram,−−−CD ⊥

−−−AC,

−−−BE ⊥

−−−AC, AE = 17,

BE = 8, and CD = 32. Find DE.

A. 45 B. 51

C. 60 D. 68

45. In the figure, RS = 6, RT = 4, and TU = 10. Whatis the length of

−−−−UV ?

A. 15

B. 9

C. 4

D. not enoughinformation

46.

Determine the length of−−−ST if

−−−−MN is (8x − 3)

units.

A. 4x − 23 B. 16x − 6

C. 4x + 32 D.

8x − 3

2

47. Which of the following ratios is the tangent of anangle?

A.opposite

hypotenuseB.

hypotenuse

adjacent

C.adjacent

hypotenuseD.

opposite

adjacent

48. Given the triangle shown, which of the followingis true?

A. sinB =cb

B. cosA =cb

C. tanA =ba

D. sinB =bc

49. Which of the following statements is incorrect for^XYZ ?

A. sinZ = 513

B. tanY = 512

C. XZ = 13

D. cosX = 513

50. In the triangle below, sinP = 513 . Find cosR.

A. 1213 B. 5

12 C. 1312 D. 5

13

51. Find the length of side x.

A. 10 B. 12

C. 14 D. 194


52. In ÂBC, AC = 10, BC = 8, m∠B = 90◦ andm∠BDA = 90◦. How long is

−−−CD ?

A. 3.6 B. 4

C. 5 D. 6.4

53. In triangle PQR, PQ = 8 cm, QR = 6 cm, andm∠PQR = 30◦. Exactly how long is

−−−PR ?

A. 100 − 48√

3

B.√

100 − 48√

3

C.√

52

D. 10 − 4√

3

54. Given:−−−QR and

−−−QS are tangents to the circle centered at P.

−−−QP intersects the circle at M.

Prove: RM = SM

statement reason

1. PR = PS

2. RQ = SQ

3. m∠QRP = m∠QSP

4. ^QRP ∼= ^QSP

5. m∠RPQ = m∠SPQ

6. RM = SM

55.

Given: ABCD is a parallelogram

Prove: AF = AB

statement reason

1. Given

2. m∠B = m∠ADC

3. m∠AFC = m∠ADC

4. both = m∠ADC

5.


56. Given:−−−−OU bisects

−−−RP

m∠OTR = 90◦

Prove:−−−TO ⊥

−−−−OU

statement reason

1. Given

2. Given

3.−−−−OU ⊥

−−−PR

4. m∠OUR = 90◦

5.

6. m∠TOU = 90◦

7.

57. In the circle shown, chords AC and BD intersectat E. If EB = x − 4, DE = 2x + 9, AE = x, andEC = x + 6. How long is

−−−BD ?

A. 26 B. 28

C. 32 D. 34

58. Find the value of x.

A. 38◦ B. 42◦

C. 71◦ D. 142◦

59. What is the measure, in degrees, of ∠B ?

A. 85 B. 89

C. 95 D. 99

60. Given the circle with center O and withm∠ROQ = 160◦, find the measure of minor arc(

PR.

A. 20◦ B. 40◦

C. 80◦ D. 210◦

61. If m∠NOM = 60◦, then what is the length of the

minor arc

(

NM ?

A. π4 B. π

C. 3π2 D. 2π


62. If r = 12 cm, what is the area of this sector?Express your answer to the nearest tenth of acentimeter.

A. 339.3 cm2

B. 361.8 cm2

C. 482.5 cm2

D. 493.6 cm2

63. Write the equation for the circle.

A. (x − 3)2 + (y − 1)2 = 9

B. (x − 3)2 + (y + 1)2 = 3

C. (x − 3)2 + (y + 1)2 =√

3

D. (x − 3)2 + (y + 1)2 = 9

64. What is the equation of a circle having radius 5and center (−3, 2) ?

A. (x + 3)2 + (y − 2)2 = 5

B. (x + 3)2 + (y − 2)2 = 25

C. (x − 3)2 + (y + 2)2 = 5

D. (x − 3)2 + (y + 2)2 = 25

65.−−−AB is the diameter of a circle where A is (2, 0)and B is (10, 8). What is the equation of thecircle?

66. What is the equation of the line perpendicular tothe line shown in the diagram that passes throughthe point (−2,−4)?

A. x + 3y = −14

B. x − 3y = 10

C. 3x − y = −2

D. 2x + 3y = −16

67. Join−−−AB on the coordinate plane. Determine the

midpoint of−−−AB.

�

��

�

A•

•B

A. (1,−1) B. (1, 0)

C. (−1, 0) D. (−1, 1)

68. One endpoint of a line segment is at (1, 2).The midpoint of the line segment is at (5, 8).Determine the coordinate of the other endpoint.

A. (−3,−4) B. (3.5, 5)

C. (6, 10) D. (9, 14)

69. Given the coordinates of X, Y , and Z, as shown inthe figure, find the perimeter of the triangle

A. 6 units

B. 11 units

C. 12 units

D. 14 units


70. The formula for area of a triangle is A = 12bh.

What is the area of the figure shown?

A. 24 square units B. 16 square units

C. 40 square units D. 20 square units

71. What is a reasonable estimate for the area of oneof the circles?

A. less than 5 cm2 B. about 10 cm2

C. about 20 cm2 D. more than 35 cm2

72. Based on the diagram below, what is a reasonableestimate for the area of the shaded region?

A. less than 4 units2 B. less than 6 units2

C. less than 7 units2 D. less than 8 units2

73. Carli created a sculpture as shown in the diagram.The sculpture is 8 centimeters tall and the area ofthe bottom of the sculpture is 49 square inches.Which expression can be used to find how muchclay Carli used to make the sculpture?

A. 8 × 49 B. 49 × 49 × 8

C. 13 × 7 × 8 D. 8 × 49 × 1

3

74. What is the 3-dimensional figure shown?

Top View Side View

A. cylinder B. cone

C. triangular pyramid D. triangular prism


75. Here is a picture of a 90◦ arc joined to a segment.The segment is the radius of the arc.

Suppose points B and C are fixed, but arc BAcan rotate in space around segment BC. If theangle between the arc and the segment does notchange, what 3-dimensional shape is created bythe rotating arc?

A. a spiral B. a cone

C. a cylinder D. a hemisphere

76. In the diagram below, a sequence of rigid motionsmaps ABCD onto JKLM.

If m∠A = 82◦, m∠B = 104◦, and m∠L = 121◦, themeasure of ∠M is

A. 53◦ B. 82◦ C. 104◦ D. 121◦

77. Parallelogram HAND is drawn below withdiagonals

−−−−HN and

−−−AD intersecting at S.

Which statement is always true?

A. HN = 12AD B. AS = 1

2AD

C. ∠AHS ∼= ∠ANS D. ∠HDS ∼= ∠NDS

78. The graph below shows two congruent triangle,ABC and A′B′C′.

Which rigid motion would map ÂBC ontoÂ′B′C′?

A. a rotation of 90 degrees counterclockwiseabout the origin

B. a translation of three units to the left andthree units up

C. a rotation of 180 degrees about the origin

D. a reflection over the line y = x


79. A man was parasailing above a lake at an angle ofelevation of 32◦ from a boat, as modeled in thediagram below.

If 129.5 meters of cable connected the boat to theparasail, approximately how many meters abovethe lake was the man?

A. 68.6 B. 80.9 C. 109.8 D. 244.4

80. A right hexagonal prism is shown below. Atwo-dimensional cross section that is perpendicularto the base is taken from the prism.

Which figure describes the two-dimensional crosssection?

A. triangle B. rectangle

C. pentagon D. hexagon

81. In the diagram below,−−−AC has endpoints with

coordinates A(−5, 2) and C(4,−10).

If B is a point on−−−AC and AB :BC = 1 : 2, what

are the coordinates of B?

A. (−2,−2) B. (− 12 ,−4)

C. (0,− 143 ) D. (1,−6)

82. An ice cream waffle cone can be modeled bya right circular cone with a base diameter of6.6 centimeters and a volume of 54.45π cubiccentimeters. What is the number of centimeters inthe height of the waffle cone?

A. 3 34 B. 5 C. 15 D. 24 3

4

83. The vertices of ^PQR have coordinates P(2, 3),Q(3, 8), and R(7, 3). Under which transformationof ^PQR are distance and angle measurepreserved?

A. (x, y)→ (2x, 3y)

B. (x, y)→ (x + 2, 3y)

C. (x, y)→ (2x, y + 3)

D. (x, y)→ (x + 2, y + 3)


84. In ÂBC shown below, side−−−AC is extended

to point D with m∠DAB = (180 − 3x)◦,m∠B = (6x − 40)◦, and m∠C = (x + 20)◦.

What is m∠BAC?

A. 20◦ B. 40◦ C. 60◦ D. 80◦

85. Circle O is centered at the origin. In the diagrambelow, a quarter of circle O is graphed.

Which three-dimensional figure is generated whenthe quarter circle is continuously rotated about they-axis?

A. cone B. sphere

C. cylinder D. hemisphere

86. Rectangle A′B′C′D′ is the image of rectangleABCD after a dilation centered at point A by ascale factor of 2

3 . Which statement is correct?

A. Rectangle A′B′C′D′ has a perimeter that is 23

the perimeter of rectangle ABCD.

B. Rectangle A′B′C′D′ has a perimeter that is 32

the perimeter of rectangle ABCD.

C. Rectangle A′B′C′D′ has an area that is the 23

area of rectangle ABCD.

D. Rectangle A′B′C′D′ has an area that is the 32

area of rectangle ABCD.

87. The equation of a circle is x2 + y2 − 6x + 2y = 6.What are the coordinates of the center and thelength of the radius of the circle?

A. center (−3, 1) and radius 4

B. center (3,−1) and radius 4

C. center (−3, 1) and radius 16

D. center (3,−1) and radius 16

88. In the diagram of ÂBC below,−−−DE is parallel to

−−−AB, CD = 15, AD = 9, and AB = 40.

The length of−−−DE is

A. 15 B. 24 C. 25 D. 30

89. The line whose equation is 3x − 5y = 4 is dilatedby a scale factor of 5

3 centered at the origin.Which statement is correct?

A. The image of the line has the same slope asthe pre-image but a different y-intercept.

B. The image of the line has the same y-interceptas the pre-image but a different slope.

C. The image of the line has the same slope andthe same y-intercept as the pre-image.

D. The image of the line has a different slopeand a different y-intercept from the pre-image.


90. Which transformation would not carry a squareonto itself?

A. a reflection over one of its diagonals

B. a 90◦ rotation clockwise about its center

C. a 180◦ rotation about one of its vertices

D. a reflection over the perpendicular bisector ofone side

91. In circle M below, diameter−−−AC, chords

−−−AB and

−−−BC, and radius

−−−−MB are drawn.

Which statement is not true?

A. ÂBC is a right triangle.

B. ÂBM is isosceles.

C. m

(

BC = m∠BMC

D. m

(

AB = 12m∠ACB

92. In the diagram below,−−−XS and

−−−YR intersect at Z.

Segments XY and RS are drawn perpendicular to−−−YR to form triangles XYZ and SRZ.


A. (XY)(SR) = (XZ)(RZ)

B. ^XYZ ∼= ^SRZ

C.−−−XS ∼=

−−−YR

D.XYSR

=YZRZ

93. As shown in the diagram below,−−−−−ABC ‖

−−−−−EFG and

−−−BF ∼=

−−−EF

If m∠CBF = 42.5◦, then m∠EBF is

A. 42.5◦ B. 68.75◦

C. 95◦ D. 137.5◦

94. A parallelogram must be a rhombus if its diagonals

A. are congruent

B. bisect each other

C. do not bisect its angles

D. are perpendicular to each other


95. What is an equation of a line which passesthrough (6, 9) and is perpendicular to the linewhose equation is 4x − 6y = 15?

A. y − 9 = − 32 (x − 6) B. y − 9 = 2

3 (x − 6)

C. y + 9 = − 32 (x + 6) D. y + 9 = 2

3 (x + 6)

96. Quadrilateral ABCD is inscribed in circle O, asshown below.

If m∠A = 80◦, m∠B = 75◦, m∠C = (y + 30)◦, andm∠D = (x − 10)◦, which statement is true?

A. x = 85 and y = 50 B. x = 90 and y = 45

C. x = 110 and y = 75 D. x = 115 and y = 70

97. A regular pyramid has a square base. Theperimeter of the base is 36 inches and the heightof the pyramid is 15 inches. What is the volumeof the pyramid in cubic inches?

A. 180 B. 405 C. 540 D. 1215

98. In the diagram below of ÂBC, ∠ABC is a rightangle, AC = 12, AD = 8, and altitude

−−−BD is drawn.

What is the length of−−−BC

A. 4√

2 B. 4√

3 C. 4√

5 D. 4√

6

99. In the diagram below, two concentric circles withcenter O, and radii

−−−−OC,

−−−−OD,

−−−−−OCE, and

−−−−−ODF are

drawn.

If OC = 4 and OE = 6, which relationship betweenthe length of arc EF and the length of arc CD isalways true?

A. The length of arc EF is 2 units longer thanthe length of arc CD.

B. The length of arc EF is 4 units longer thanthe length of arc CD.

C. The length of arc EF is 1.5 times the lengthof arc CD.

D. The length of arc EF is 2.0 times the lengthof arc CD.

100. Given: Parallelogram ABCD with diagonal−−−AC

drawn

Prove: ÂBC ∼= ^CDA


101. The diagram below shows circle O with diameter−−−AB. Using a compass and straightedge, constructa square that is inscribed in circle O. [Leave allconstruction marks.]

102. Given: Right triangle ABC with right angle at C

If sinA increases, does cosB increase or decrease?Explain why.

103. In the diagram below, the circle has a radius of25 inches. The area of the unshaded sector is500π in2.

Determine and state the degree measure ofangle Q, the central angle of the shaded sector.

104. A machinist creates a solid steel part for awind turbine engine. The part has a volume of1015 cubic centimeters. Steel can be purchasedfor $0.29 per kilogram, and has a density of7.95 g/cm3.

If the machinist makes 500 of these parts, what isthe cost of the steel, to the nearest dollar?

105. In the graph below, ÂBC has coordinatesA(−9, 2), B(−6,−6), and C(−3,−2), and ^RSThas coordinates R(−2, 9), S(5, 6), and T(2, 3).

Is ÂBC congruent to ^RST? Use the propertiesof rigid motions to explain your reasoning.

106. Bob places an 18-foot ladder 6 feet from the baseof his house and leans it up against the side of hishouse. Find, to the nearest degree, the measure ofthe angle the bottom of the ladder makes with theground.


107. Triangle ABC and triangle ADE are graphed onthe set of axes below.

Describe a transformation that maps triangle ABConto triangle ADE.

Explain why this transformation makestriangle ADE similar to triangle ABC.

108. A storage tank is in the shape of a cylinder with ahemisphere on the top. The highest point on theinside of the storage tank is 13 meters above thefloor of the storage tank, and the diameter insidethe cylinder is 8 meters. Determine and state, tothe nearest cubic meter, the total volume insidethe storage tank.

109. As shown in the diagram below, an island (I) isdue north of a marina (M). A boat house (H) is4.5 miles due west of the marina. From the boathouse, the island is located at an angle of 54◦

from the marina.

Determine and state, to the nearest tenth of a mile,the distance from the boat house (H) to the island(I).

Determine and state, to the nearest tenth of a mile,the distance from the island (I) to the marina (M).

110. In the coordinate plane, the vertices oftriangle PAT are P(−1,−6), A(−4, 5), andT(5,−2). Prove that ^PAT is an isoscelestriangle.

State the coordinates of R so that quadrilateralPART is a parallelogram.

Prove that quadrilateral PART is a parallelogram.


111. A two-dimensional cross section is taken of athree-dimensional object. If this cross section isa triangle, what can not be the three-dimensionalobject?

A. cone B. cylinder

C. pyramid D. rectangular prism

112. The image of ^DEF is ^D′E′F′. Under whichtransformation will the triangles not be congruent?

A. a reflection through the origin

B. a reflection over the line y = x

C. a dilation with a scale factor of 1 centered at(2, 3)

D. dilation with a scale factor of 32 centered at

the origin

113. The vertices of square RSTV have coordinatesR(−1, 5), S(−3, 1), T(−7, 3), and V(−5, 7). Whatis the perimeter of RSTV?

A.√

20 B.√

40 C. 4√

20 D. 4√

40

114. In the diagram below of circle O, chord−−−CD is

parallel to diameter−−−−−AOB and m

(

CD = 130.

What is m

(

AC?

A. 25 B. 50 C. 65 D. 115

115. In the diagram below,−−−AD intersects

−−−BE at C, and

−−−AB ‖

−−−DE.

If CD = 6.6 cm, DE = 3.4 cm, CE = 4.2 cm, andBC = 5.25 cm, what is the length of

−−−AC, to the

nearest hundredth of a centimeter?

A. 2.70 B. 3.34 C. 5.28 D. 8.25

116. As shown in the graph below, the quadrilateral isa rectangle.

Which transformation would not map the rectangleonto itself?

A. a reflection over the x-axis

B. a reflection over the line x = 4

C. a rotation of 180◦ about the origin

D. a rotation of 180◦ about the point (4, 0)


117. In the diagram below, triangle ACD has points Band E on sides

−−−AC and

−−−AD, respectively, such that

−−−BE ‖

−−−CD, AB = 1, BC = 3.5, and AD = 18.

What is the length of−−−AE, to the nearest tenth?

A. 14.0 B. 5.1 C. 3.3 D. 4.0

118. In the diagram below of parallelogram ROCK,m∠C is 70◦ and m∠ROS is 65◦.

What is m∠KSO?

A. 45◦ B. 110◦ C. 115◦ D. 135◦

119. In the diagram below, ∠GRS ∼= ∠ART , GR = 36,SR = 45, AR = 15, and RT = 18.

Which triangle similarity statement is correct?

A. ^GRS ∼ ART by AA.

B. ^GRS ∼ ART by SAS.

C. ^GRS ∼ ART by SSS.

D. ^GRS is not similar to ÂRT .

120. The line represented by the equation 4y = 3x + 7is transformed by a dilation centered at the origin.Which linear equation could represent its image?

A. 3x − 4y = 9 B. 3x + 4y = 9

C. 4x − 3y = 9 D. 4x + 3y = 9

121. Given ÂBC with m∠B = 62◦ and side−−−AC

extended to D, as shown below.

Which value of x makes−−−AB ∼=

−−−CB?

A. 59◦ B. 62◦ C. 118◦ D. 121◦

122. In the diagram shown below,−−−PA is tangent to

circle T at A, and secant−−−−−PBC is drawn where

point B is on circle T .

If PB = 3 and BC = 15, what is the length of−−−PA?

A. 3√

5 B. 3√

6 C. 3 D. 9

123. A rectangle whose length and width are 10 and6, respectively, is shown below. The rectangle iscontinuously rotated around a straight line to forman object whose volume is 150π.

Which line could the rectangle be rotated around?

A. a long side

B. a short side

C. the vertical line of symmetry

D. the horizontal line of symmetry


124. If ABCD is a parallelogram, which statementwould prove that ABCD is a rhombus?

A. ∠ABC ∼= ∠CDA B.−−−AC ∼=

−−−BD

C.−−−AC ⊥

−−−BD D.

−−−AB ⊥

−−−CD

125. To build a handicapped-access ramp, the buildingcode states that for every 1 inch of vertical risein height, the ramp must extend out 12 incheshorizontally, as shown in the diagram below.

What is the angle of inclination, x, of this ramp,to the nearest hundredth of a degree?

A. 4.76 B. 4.78 C. 85.22 D. 85.24

126. In the diagram below of ÂBC, D, E, and F arethe midpoints of

−−−AB,−−−BC, and

−−−CA, respectively.

What is the ratio of the area of ^CFE to the areaof ^CAB?

A. 1 : 1 B. 1 : 2 C. 1 : 3 D. 1 : 4

127. The coordinates of the endpoints of−−−AB are

A(−8,−2) and B(16, 6). Point P is on−−−AB. What

are the coordinates of point P, such that AP :PBis 3 : 5?

A. (1, 1) B. (7, 3)

C. (9.6, 3.6) D. (6.4, 2.8)

128. Kirstie is testing values that would make triangleKLM a right triangle when

−−−LN is an altitude, and

KM = 16, as shown below.

Which lengths would make triangle KLM a righttriangle?

A. LM = 13 and KN = 6

B. LM = 12 and NM = 9

C. KL = 11 and KN = 7

D. LN = 8 and NM = 10

129. In right triangle ABC, m∠A = 32◦, m∠B = 90◦,and AC = 6.2 cm. What is the length of

−−−BC, to

the nearest tenth of a centimeter?

A. 3.3 B. 3.9 C. 5.3 D. 11.7

130. The 2010 U.S. Census populations and populationdensities are shown in the table below.

State Population Density

(people

mi2

)Population in

2010

Florida 350.6 18,801,310

Illinois 231.1 12,830,632

New York 411.2 19,378,102

Pennsylvania 283.9 12,702,379

Based on the table above, which list has the states’areas, in square miles, in order from largest tosmallest?

A. Illinois, Florida, New York, Pennsylvania

B. New York, Florida, Illinois, Pennsylvania

C. New York, Florida, Pennsylvania, Illinois

D. Pennsylvania, New York, Florida, Illinois


131. In a right triangle, sin (40 − x)◦ = cos (3x)◦. Whatis the value of x?

A. 10 B. 15 C. 20 D. 25

132. A regular decagon is rotated n degrees about itscenter, carrying the decagon onto itself. The valueof n could be

A. 10◦ B. 150◦ C. 225◦ D. 252◦

133. In a circle with a diameter of 32, the area of a

sector is512π

3. The measure of the angle of the

sector, in radians, is

A. π3 B. 4π

3 C. 16π3 D. 64π

3

134. What is an equation of the perpendicular bisectorof the line segment shown in the diagram below?

A. y + 2x = 0 B. y − 2x = 0

C. 2y + x = 0 D. 2y − x = 0

135. Sue believes that the two cylinders shown in thediagram below have equal volumes.

Is Sue correct? Explain why.

136. In the diagram of rhombus PQRS below, thediagonals

−−−PR and

−−−QS intersect at point T , PR = 16,

and QS = 30. Determine and state the perimeterof PQRS.


137. Quadrilateral MATH and its image M′′A′′T ′′H′′ aregraphed on the set of axes below.

Describe a sequence of transformations that mapsquadrilateral MATH onto quadrilateral M′′A′′T ′′H′′.

138. Using a compass and straightedge, construct aregular hexagon inscribed in circle O. [Leave allconstruction marks.]

139. The coordinates of the endpoints of−−−AB are A(2, 3)

and B(5,−1). Determine the length of−−−−A′B′, the

image of−−−AB, after a dilation of 1

2 centered at theorigin.

140. In the diagram below of ÂBC and ^XYZ, asequence of rigid motions maps ∠A onto ∠X, ∠Conto ∠Z, and

−−−AC onto

−−−XZ.

Determine and state whether−−−BC ∼=

−−−YZ. Explain

why.

141. Determine and state the coordinates of the centerand the length of the radius of a circle whoseequation is x2 + y2 − 6x = 56 − 8y.


142. Triangle PQR has vertices P(−3,−1), Q(−1, 7),and R(3, 3), and points A and B are midpoints of−−−PQ and

−−−RQ, respectively. Use coordinate geometry

to prove that−−−AB is parallel to

−−−PR and is half the

length of−−−PR.

143. In the diagram below of circle O, tangent−−−EC is

drawn to diameter−−−AC. Chord

−−−BC is parallel to

secant−−−−−ADE, and chord

−−−AB is drawn.

Prove:BCCA

=ABEC

144. Keira has a square poster that she is framing andplacing on her wall. The poster has a diagonal58 cm long and fits exactly inside the frame. Thewidth of the frame around the picture is 4 cm.

Determine and state the total area of the poster andframe to the nearest tenth of a square centimeter.

145. Isosceles trapezoid ABCD has bases−−−−DC and

−−−AB

with nonparallel legs−−−AD and

−−−BC. Segments

AE, BE, CE, and DE are drawn in trapezoidABCD such that ∠CDE ∼= ∠DCE,

−−−AE ⊥

−−−DE, and

−−−BE ⊥

−−−CE.

Prove ÂDE ∼= ^BCE and prove ÂEB is anisosceles triangle.


146. A rectangular in-ground pool is modeled by theprism below. The inside of the pool is 16 feetwide and 35 feet long. The pool has a shallowend and a deep end, with a sloped floor connectingthe two ends. Without water, the shallow end is9 feet long and 4.5 feet deep, and the deep end ofthe pool is 12.5 feet long.

a) If the sloped floor has an angle of depressionof 16.5 degrees, what is the depth of thepool at the deep end, to the nearest tenth ofa foot?

b) Find the volume of the inside of the pool tothe nearest cubic foot.

c) A garden hose is used to fill the pool.Water comes out of the hose at a rate of10.5 gallons per minute. How much time, tothe nearest hour, will it take to fill the pool6 inches from the top? [1 ft3 = 7.48 gallons]

147. In the diagram below, ÂBC ∼= ^DEF.

Which sequence of transformations maps ÂBConto ^DEF?

A. a reflection over the x-axis followed by atranslation

B. a reflection over the y-axis followed by atranslation

C. a rotation of 180◦ about the origin followedby a translation

D. a counterclockwise rotation of 90◦ about theorigin followed by a translation


148. On the set of axes below, the vertices of ^PQRhave coordinates P(−6, 7), Q(2, 1), and R(−1,−3).

What is the area of ^PQR?

A. 10 B. 20 C. 25 D. 50

149. In right triangle ABC, m∠C = 90◦. If cosB = 513 ,

which function also equals 513?

A. tanA B. tanB C. sinA D. sinB

150. In the diagram below, m

(ABC = 268◦.

What is the number of degrees in the measure of∠ABC?

A. 134◦ B. 92◦ C. 68◦ D. 46◦

151. Given ^MRO shown below, with trapezoid PTRO,MR = 9, MP = 2, and PO = 4.

What is the length of−−−TR?

A. 4.5 B. 5 C. 3 D. 6

152. A line segment is dilated by a scale factor of2 centered at a point not on the line segment.Which statement regarding the relationship betweenthe given line segment and its image is true?

A. The line segments are perpendicular, and theimage is one-half of the length of the givenline segment.

B. The line segments are perpendicular, and theimage is twice the length of the given linesegment.

C. The line segments are parallel, and the imageis twice the length of the given line segment.

D. The line segments are parallel, and the imageis one-half of the length of the given linesegment.

153. Which figure always has exactly four lines ofreflection that map the figure onto itself?

A. square B. rectangle

C. regular octagon D. equilateral triangle


154. In the diagram below of circle O, chord−−−DF

bisects chord−−−BC at E.

If BC = 12 and FE is 5 more than DE, then FE is

A. 13 B. 9 C. 6 D. 4

155. Kelly is completing a proof based on the figurebelow.

She was given that ∠A ∼= ∠EDF, and has alreadyproven

−−−AB ∼=

−−−DE. Which pair of corresponding

parts and triangle congruency method would notprove ÂBC ∼= ^DEF?

A.−−−AC ∼=

−−−DF and SAS

B.−−−BC ∼=

−−−EF and SAS

C. ∠C ∼= ∠F and AAS

D. ∠CBA ∼= ∠FED and ASA

156. In the diagram below,−−−DE divides

−−−AB and

−−−AC

proportionally, m∠C = 26◦, m∠A = 82◦, and−−−DF

bisects ∠BDE.

The measure of angle DFB is

A. 36◦ B. 54◦ C. 72◦ D. 82◦

157. Which set of statements would describe aparallelogram that can always be classified as arhombus?

I. Diagonals are perpendicular bisectors ofeach other.

II. Diagonals bisect the angles from whichthey are drawn.

III. Diagonals form four congruent isoscelesright triangles.

A. I and II B. I and III

C. II and III D. I, II, and III

158. The equation of a circle is x2 + y2 − 12y + 20 = 0.What are the coordinates of the center and thelength of the radius of the circle?

A. center (0, 6) and radius 4

B. center (0,−6) and radius 4

C. center (0, 6) and radius 16

D. center (0,−6) and radius 16


159. In the diagram of ^RST below, m∠T = 90◦,RS = 65, and ST = 60.

What is the measure of ∠S, to the nearest degree?

A. 23◦ B. 43◦ C. 47◦ D. 67◦

160. Triangle A′B′C is the image of ÂBC after adilation followed by a translation.

Which statement(s) would always be true withrespect to this sequence of transformations?

I. ÂBC ∼= Â′B′C′

II. ÂBC ∼ Â′B′C′

III.−−−AB ‖

−−−−A′B′

IV. AA′ = BB′

A. II, only B. I and II

C. II and III D. II, III, and IV

161. Line segment RW has endpoints R(−4, 5) andW(6, 20). Point P is on

−−−−RW such that RP :PW is

2 : 3. What are the coordinates of point P?

A. (2, 9) B. (0, 11) C. (2, 14) D. (10, 2)

162. The pyramid shown below has a square base, aheight of 7, and a volume of 84.

What is the length of the side of the base?

A. 6 B. 12 C. 18 D. 36

163. In the diagram below of triangle MNO, ∠M and∠O are bisected by

−−−MS and

−−−OR, respectively.

Segments MS and OR intersect at T , andm∠N = 40◦.

If m∠TMR = 28◦, the measure of angle OTS is

A. 40◦ B. 50◦ C. 60◦ D. 70◦

164. In the diagram below, right triangle ABC has legswhose lengths are 4 and 6.

What is the volume of the three-dimensionalobject formed by continuously rotating the righttriangle around

−−−AB?

A. 32π B. 48π C. 96π D. 144π


165. What is an equation of a line that is perpendicularto the line whose equation is 2y = 3x − 10 andpasses through (−6, 1)?

A. y = − 23x − 5 B. y = − 2

3x − 3

C. y = 23x + 1 D. y = 2

3x + 10

166. In quadrilateral BLUE shown below,−−−BE ∼=

−−−UL.

Which information would be sufficient to provequadrilateral BLUE is a parallelogram?

A.−−−BL ‖

−−−EU B.

−−−LU ‖

−−−BE

C.−−−BE ∼=

−−−BL D.

−−−LU ∼=

−−−EU

167. A ladder 20 feet long leans against a building,forming an angle of 71◦ with the level ground.To the nearest foot, how high up the wall of thebuilding does the ladder touch the building?

A. 15 B. 16 C. 18 D. 19

168. In the two distinct acute triangles ABC and DEF,∠B = ∠E. Triangles ABC and DEF are congruentwhen there is a sequence of rigid motions thatmaps

A. ∠A onto ∠D, and ∠C onto ∠F

B.−−−AC onto

−−−DF, and

−−−BC onto

−−−EF

C. ∠C onto ∠F, and−−−BC onto

−−−EF

D. point A onto point D, and−−−AB onto

−−−DE

169. A fabricator is hired to make a 27-foot-long solidmetal railing for the stairs at the local library. Therailing is modeled by the diagram below. Therailing is 2.5 inches high and 2.5 inches wideand is comprised of a rectangular prism and ahalf-cylinder.

How much metal, to the nearest cubic inch, willthe railing contain?

A. 151 B. 795 C. 1808 D. 2025

170. In the diagram below, AC = 7.2 and CE = 2.4.

Which statement is not sufficient to proveÂBC ∼ ÊDC?

A.−−−AB ‖

−−−ED

B. DE = 2.7 and AB = 8.1

C. CD = 3.6 and BC = 10.8

D. DE = 3.0, AB = 9.0, CD = 2.9, and BC = 8.7

171. Given: Trapezoid JKLM with−−−JK ‖

−−−ML.

Using a compass and straightedge, construct thealtitude from vertex J to

−−−ML.


172. Determine and state, in terms of π, the area of asector that intercepts a 40◦ arc of a circle with aradius of 4.5.

173. The diagram below shows two figures. Figure A isa right triangular prism and figure B is an obliquetriangular prism. The base of figure A has a heightof 5 and a length of 8 and the height of prism Ais 14. The base of figure B has a height of 8 anda length of 5 and the height of prism B is 14.

Figure A Figure B

Use Cavalieri’s Principle to explain why thevolumes of these two triangular prisms are equal.

174. When volleyballs are purchased, they are notfully inflated. A partially inflated volleyballcan be modeled by a sphere whose volume isapproximately 180 in3. After being fully inflated,its volume is approximately 294 in3. To thenearest tenth of an inch, how much does the radiusincrease when the volleyball is fully inflated?

175. In right triangle ABC shown below, altitude−−−CD is

drawn to hypotenuse−−−AB.

Explain why ÂBC ∼ ÂCD.

176. Triangle ABC and triangle DEF are drawn below.

If AB ∼= DE, AC ∼= DF, and ∠A ∼= ∠D,write a sequence of transformations that mapstriangle ABC onto triangle DEF.

177. Line n is represented by the equation 3x+ 4y = 20.Determine and state the equation of line p, theimage of line n, after a dilation of scale factor 1

3centered at the point (4, 2).

Explain your answer.


178. Triangle ABC has vertices at A(−5, 2), B(−4, 7),and C(−2, 7), and triangle DEF has vertices atD(3, 2), E(2, 7), and F(0, 7). Graph and labelÂBC and ^DEF on the set of axes below.

Determine and state the single transformationwhere ^DEF is the image of ÂBC.

Use your transformation to explain whyÂBC ∼= ^DEF.

179. Given:−−−RS

and−−−TV

bi-secteachotheratpoint X

−−−TR

and−−−SV

aredrawn

Prove:−−−TR‖−−−SV

180. A gas station has a cylindrical fueling tank thatholds the gasoline for its pumps, as modeledbelow. The tank holds a maximum of 20,000gallons of gasoline and has a length of 34.5 feet.

A metal pole is used to measure how much gas isin the tank. To the nearest tenth of a foot, howlong does the pole need to be in order to reachthe bottom of the tank and still extend one footoutside the tank? Justify your answer. [1 ft3 =7.48 gallons]


181. Quadrilateral PQRS has vertices P(−2, 3), Q(3, 8),R(4, 1), and S(−1,−4).

Prove that PQRS is a rhombus.

Prove that PQRS is not a square.

182. Freda, who is training to use a radar system,detects an airplane flying at a constant speed andheading in a straight line to pass directly over herlocation. She sees the airplane at an angle ofelevation of 15◦ and notes that it is maintaining aconstant altitude of 6250 feet. One minute later,she sees the airplane at an angle of elevation of52◦. How far has the airplane traveled, to thenearest foot?

Determine and state the speed of the airplane, tothe nearest mile per hour.

183. A student has a rectangular postcard that he foldsin half lengthwise. Next, he rotates it continuouslyabout the folded edge. Which three-dimensionalobject below is generated by this rotation?

A. B.

C. D.

184. A three-inch line segment is dilated by a scalefactor of 6 and centered at its midpoint. What isthe length of its image?

A. 9 inches B. 2 inches

C. 15 inches D. 18 inches

185. Kevin’s work for deriving the equation of a circleis shown below.

x2 + 4x = −(y2 − 20)

STEP 1 x2 + 4x = −y2 + 20

STEP 2 x2 + 4x + 4 = −y2 + 20 − 4

STEP 3 (x + 2)2 = −y2 + 20 − 4

STEP 4 (x + 2)2 + y2 = 16

In which step did he make an error in his work?

A. Step 1 B. Step 2

C. Step 3 D. Step 4


186. Which transformation of−−−OA would result in an

image parallel to−−−OA?

A. a translation of two units down

B. a reflection over the x-axis

C. a reflection over the y-axis

D. a clockwise rotation of 90◦ about the origin

187. Using the information given below, which set oftriangles can not be proven similar?

A.

B.

C.

D.

188. A company is creating an object from a woodencube with an edge length of 8.5 cm. A rightcircular cone with a diameter of 8 cm and analtitude of 8 cm will be cut out of the cube.Which expression represents the volume of theremaining wood?

A. (8.5)3 − π(8)2(8) B. (8.5)3 − π(4)2(8)

C. (8.5)3 − 13π(8)2(8) D. (8.5)3 − 1

3π(4)2(8)

189. Two right triangles must be congruent if

A. an acute angle in each triangle is congruent

B. the lengths of the hypotenuses are equal

C. the corresponding legs are congruent

D. the areas are equal

190. Which sequence of transformations will mapÂBC onto Â′B′C ′?

A. reflection and translation

B. rotation and reflection

C. translation and dilation

D. dilation and rotation


191. In parallelogram ABCD, diagonals−−−AC and

−−−BD

intersect at E. Which statement does not proveparallelogram ABCD is a rhombus?

A.−−−AC ∼=

−−−DB B.

−−−AB ∼=

−−−BC

C.−−−AC ⊥

−−−DB D.

−−−AC bisects ∠DCB.

192. In the diagram below of circle O,−−−OB and

−−−−OC are

radii, and chords−−−AB,−−−BC, and

−−−AC are drawn.

Which statement must always be true?

A. ∠BAC ∼= ∠BOC

B. m∠BAC = 12m∠BOC

C. ^BAC and ^BOC are isosceles.

D. The area of ^BAC is twice the area of^BOC.

193. A 20-foot support post leans against a wall,making a 70◦ angle with the ground. To thenearest tenth of a foot, how far up the wall willthe support post reach?

A. 6.8 B. 6.9 C. 18.7 D. 18.8

194. Line segment NY has endpoints N(−11, 5)and Y(5,−7). What is the equation of theperpendicular bisector of

−−−NY?

A. y + 1 = 43 (x + 3) B. y + 1 = − 3

4 (x + 3)

C. y − 6 = 43 (x − 8) D. y − 6 = − 3

4 (x − 8)

195. In ^RST shown below, altitude−−−SU is drawn to

−−−RT at U.

If SU = h, UT = 12, and RT = 42, which value ofh will make ^RST a right triangle with ∠RST asa right angle?

A. 6√

3 B. 6√

10 C. 6√

14 D. 6√

35

196. In the diagram below, ÂBC has vertices A(4, 5),B(2, 1), and C(7, 3).

What is the slope of the altitude drawn from A to−−−BC?

A. 25 B. 3

2 C. − 12 D. − 5

2

197. In the diagram below, ÊRM ∼ ^JTM.


A. cos J =RMRE

B. cosR =JMJT

C. tanT =RMEM

D. tanE =TMJM


198. On the set of axes below, rectangle ABCD can beproven congruent to rectangle KLMN using whichtransformation?

A. rotation

B. translation

C. reflection over the x-axis

D. reflection over the y-axis

199. In the diagram below,−−−DB and

−−−AF intersect at

point C, and−−−AD and

−−−−−FBE are drawn.

If AC = 6, DC = 4, FC = 15, m∠D = 65◦, andm∠CBE = 115◦, what is the length of

−−−CB?

A. 10 B. 12 C. 17 D. 22.5

200. Seawater contains approximately 1.2 ounces ofsalt per liter on average. How many gallons ofseawater, to the nearest tenth of a gallon, wouldcontain 1 pound of salt?

A. 3.3 B. 3.5 C. 4.7 D. 13.3


Problem-Attic format version 4.4.316c_ 2011–2017 EducAide Software

Licensed for use by [email protected] of Use at www.problem-attic.com

Geometry Regents Review 6/10/2018

1.Answer: AObjective: G.CO.1


3.Answer: BObjective: G.CO.1

4.Answer: DObjective: G.CO.2






10.Answer: CObjective: G.CO.2










20.Answer: [proof]Objective: G.CO.9








Teacher’s Key Page 2



30.Answer: Neither is correctObjective: G.CO.10

31.Answer: 4. DB = BE; 5. Reflective property;

6.^DBC ∼= ÊBA,SAS; CPCTCObjective: G.CO.10

32.Answer: 1.

−−−AC ∼=

−−−BC; 2. defn. of angle bisector;

4. ÂCP ∼= ^BCP, SAS; 5. CPCTCObjective: G.CO.10










42.Answer: CObjective: G.SRT.5

43.Answer: CObjective: G.SRT.5

44.Answer: BObjective: G.SRT.5

45.Answer: AObjective: G.SRT.5

46.Answer: DObjective: G.SRT.5








54.Answer: [proof]Objective: G.C.1

55.Answer: [proof]Objective: G.C.1

56.Answer:Objective: G.C.1

57.Answer: CObjective: G.C.2


58.Answer: AObjective: G.C.2



61.Answer: BObjective: G.C.5


63.Answer: AObjective: G.GPE.1

64.Answer: BObjective: G.GPE.1

65.Answer: (x − 6)2 + (y − 4)2 = 32Objective: G.GPE.1

66.Answer: BObjective: G.GPE.5

67.Answer: AObjective: G.GPE.6

68.Answer: DObjective: G.GPE.6

69.Answer: CObjective: G.GPE.7

70.Answer: DObjective: G.GPE.7

71.Answer: CObjective: G.GMD.1

72.Answer: AObjective: G.GMD.1

73.Answer: DObjective: G.GMD.3

74.Answer: BObjective: G.GMD.4

75.Answer: DObjective: G.GMD.4

76.Answer: A

77.Answer: B

78.Answer: D

79.Answer: A

80.Answer: B

81.Answer: A

82.Answer: C

83.Answer: D

84.Answer: C

85.Answer: D

86.Answer: A

87.Answer: B

88.Answer: C

89.Answer: A

90.Answer: C

91.Answer: D

92.Answer: D

93.Answer: B

94.Answer: D


95.Answer: A

96.Answer: D

97.Answer: B

98.Answer: B

99.Answer: C

100.Answer: [proof]

101.Answer:

102.Answer: Since sine and cosine are cofunctions

and ∠A and ∠B are complementary,sin A = cos B. Therefore when sinAincreases cosB increases

103.Answer: 72◦

104.Answer: $1,170

105.Answer: No

106.Answer: ≈ 71◦

107.Answer: ÂBC is dilated by a scale factor of 3

centered at point A

108.Answer: v ≈ 586 m3

109.Answer: 7.7 Mi; 6.2 Mi

110.Answer:

^PAT is isosceles because AT = PA;(2, 9); [proof]

111.Answer: B

112.Answer: D

113.Answer: C

114.Answer: A

115.Answer: D

116.Answer: C

117.Answer: D

118.Answer: D

119.Answer: D

120.Answer: A

121.Answer: D

122.Answer: B

123.Answer: C

124.Answer: C

125.Answer: A

126.Answer: D


127.Answer: A

128.Answer: B

129.Answer: A

130.Answer: A

131.Answer: D

132.Answer: D

133.Answer: B

134.Answer: D

135.Answer: Yes

136.Answer: 68

137.Answer: Reflection over the origin and a

translastion of (x − 1, y + 1)

138.Answer: [construction]

139.Answer: 2.5

140.Answer:

−−−BC ∼=

−−−YZ

141.Answer: Center (3,−4) and radius 9

142.Answer: [proof]

143.Answer: [task]

144.Answer: 2402.2

145.Answer: [task]

146.Answer: 8.5; 3752; 41

147.Answer: B

148.Answer: C

149.Answer: C

150.Answer: D

151.Answer: D

152.Answer: C

153.Answer: A

154.Answer: B

155.Answer: B

156.Answer: B

157.Answer: D

158.Answer: A

159.Answer: A

160.Answer: A

161.Answer: B

162.Answer: A

163.Answer: D

164.Answer: A

165.Answer: B

166.Answer: B

167.Answer: D

168.Answer: A

169.Answer: C

170.Answer: A


171.Answer: [construction]

172.Answer: 2.25π

173.Answer: The volume of both triangular prisms are

equal because Cavalieri’s Principle statesthat if the base area and cross sectionof both prisms are the same, then thevolumes are the same.

174.Answer: 0.6 inches

175.Answer: [explanation]

176.Answer: A translation along vector

−→CF so C maps

onto F, followed by a rotation about Fthat maps

−−−AB to

−−−DE and

−−−AC to

−−−DF.

177.Answer: y = − 3

4x + 5

178.Answer: [construction], [task], [explanation]

179.Answer: [proof]

180.Answer: 10.9 feet

181.Answer: [proof]; [proof]

182.Answer: 18,442 feet; 210 mph

183.Answer: C

184.Answer: D

185.Answer: B

186.Answer: A

187.Answer: C

188.Answer: D

189.Answer: C

190.Answer: D

191.Answer: A

192.Answer: B

193.Answer: D

194.Answer: A

195.Answer: B

196.Answer: D

197.Answer: D

198.Answer: C

199.Answer: A

200.Answer: B

Documents

Geometry Regents Review Name: DateGiven: AB = BC Dis the midpoint of AB Eis the midpoint of CB Prove: AE = DC statement reason 1. AB = BC given 2. DB = 1 2 (AB) defn. of midpoint 3