Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Countdown to Regents

------------- Day 1 -----------

1. If MNP VWX and PM is the shortest side ofMNP, what is the shortest side of VWX ?

a. XV

b. WX

c. VW

d. NP

2. What is the equation of the circle with its center at(1,2) and that passes through the point (1,2)?

a. (x 1)2 (y 2)2 4

b. (x 1)2 (y 2)2 4

c. (x 1)2 (y 2)2 2

d. (x 1)2 (y 2)2 2

3. In ABC, mA x 2 12, mB 11x 5, andmC 13x 17. Determine the longest side of

ABC.

Answer:_______________

4. What is an equation of the circle with center (5,4)and a radius of 7?

a. (x 5)2 (y 4)2 14

b. (x 5)2 (y 4)2 49

c. (x 5)2 (y 4)2 14

d. (x 5)2 (y 4)2 49

5. Given the statement: One is a prime number.What is the negation and the truth value of thenegation?a. One is not a prime number; trueb. One is not a prime number; falsec. One is a composite number; trued. One is a composite number; false

------------ Day 2 -----------

6. If the vertices of ABC are A(2,4), B(2,8), andC(5,6), then ABC is classified asa. rightb. scalenec. isoscelesd. equilateral

7. Triangle ABC shown below is a right triangle with

altitude AD drawn to the hypotenuse BC .

If BD 2 and DC 10, what is the length of AB?

a. 2 2

b. 2 5

c. 2 6

d. 2 30

8. Two prisms have equal heights and equal volumes.The base of one is a pentagon and the base of theother is a square. If the area of the pentagonal baseis 36 square inches, how many inches are in thelength of each side of the square base?a. 6b. 9c. 24d. 36

9. The solution of the system of equations y x 2 2and y x isa. (1,1) and (2,2)b. (2,2) and (1,1)c. (1,1) and (2,2)d. (2,2) and (1,1)

Name: ________________________ ID: A

2

------------- Day 3 -----------

10. Which set of numbers could not represent thelengths of the sides of a right triangle?

a. {1,3, 10}b. {2,3,4}c. {3,4,5}d. {8,15,17}

11. In a park, two straight paths intersect. The citywants to install lampposts that are both equidistantfrom each path and also 15 feet from theintersection of the paths. How many lampposts areneeded?a. 1b. 2c. 3d. 4

12. In circle O shown in the diagram below, chords AB

and CD are parallel.

If mAB 104 and mCD 168, what is mBD ?a. 38b. 44c. 88d. 96

13. A right prism has a square base with an area of 12square meters. The volume of the prism is 84 cubicmeters. Determine and state the height of theprism, in meters.

Answer:______________

-------------- Day 4 ------------

14. The equations x 2 y 2 25 and y 5 are graphedon a set of axes. What is the solution of thissystem?a. (0,0)b. (5,0)c. (0,5)d. (5,5)

15. In right triangle ABC shown in the diagram below,

altitude BD is drawn to hypotenuse AC, CD 12,and AD 3.

What is the length of AB?

a. 5 3b. 6

c. 3 5d. 9

16. In ABC, mA 60, mB 80, and mC 40.Which inequality is true?a. AB BCb. AC BCc. AC BAd. BC BA

17. What is the converse of “If an angle measures 90degrees, then it is a right angle”?a. If an angle is a right angle, then it measures 90

degrees.b. An angle is a right angle if it measures 90

degrees.c. If an angle is not a right angle, then it does not

measure 90 degrees.d. If an angle does not measure 90 degrees, then it

is not a right angle.

Name: ________________________ ID: A

3

---------- Day 5 ----------

18. Which equation represents circle O shown in thegraph below?

a. x 2 (y 2)2 10

b. x 2 (y 2)2 10

c. x 2 (y 2)2 25

d. x 2 (y 2)2 25

19. What are the coordinates of A, the image ofA(3,4), after a rotation of 180º about the origin?a. (4,3)b. (4,3)c. (3,4)d. (3,4)

20. In trapezoid RSTV with bases RS and VT ,

diagonals RT and SV intersect at Q.

If trapezoid RSTV is not isosceles, which triangle isequal in area to RSV?a. RQVb. RSTc. RVTd. SVT

21. Quadrilateral ABCD with vertices A(7,4),B(3,6),C(3,0), and D(1,8) is graphed on the setof axes below. Quadrilateral MNPQ is formed by

joining M, N, P, and Q, the midpoints of AB, BC ,

CD, and AD, respectively.

Prove that quadrilateral MNPQ is a parallelogram.

Prove that quadrilateral MNPQ is not a rhombus.

.

Name: ________________________ ID: A

4

------------ Day 6 -----------

22. Transversal EF

intersects AB

and CD

, as shownin the diagram below.

Which statement could always be used to prove

AB

CD

?a. 2 4b. 7 8c. 3 and 6 are supplementaryd. 1 and 5 are supplementary

23. In the diagram below, AC and BC are tangent tocircle O at A and B, respectively, from externalpoint C.

If mACB 38, what is mAOB?a. 71b. 104c. 142d. 161

24. What is the perimeter of a square whose diagonal is

3 2?a. 18b. 12c. 9d. 6

25. What is the measure of the largest exterior anglethat any regular polygon can have?a. 60ºb. 90ºc. 120ºd. 360º

26. In the diagram of circle O below, diameter RS ,

chord AS , tangent TS

, and secant TAR are drawn.

Complete the following proof to show

(RS)2 RA RT

27. What are the coordinates of the center of a circle ifthe endpoints of its diameter are A(8,4) andB(3,2)?a. (2.5,1)b. (2.5,1)c. (5.5,3)d. (5.5,3)

Name: ________________________ ID: A

5

---------------- Day 7 ------------

28. Which equation represents a line that is parallel tothe line whose equation is 3x 2y 7?

a. y 32

x 5

b. y 23

x 4

c. y 32

x 5

d. y 23

x 4

29. As shown below, the medians of ABC intersectat D.

If the length of BE is 12, what is the length of BD?a. 8b. 9c. 3d. 4

30. Secants JKL and JMN are drawn to circle O froman external point, J. If JK 8, LK 4, and

JM 6, what is the length of JN ?a. 16b. 12c. 10d. 8

31. In the diagram of MAH below, MH AH and medians AB and MT are drawn.Prove: MBA ATM

Statement Reason

Name: ________________________ ID: A

6

--------------- Day 8 ------------

32. What is the equation of a line passing through thepoint (6,1) and parallel to the line whose equationis 3x 2y 4?

a. y 23

x 5

b. y 23

x 3

c. y 32

x 8

d. y 32

x 5

33. Lines m and n are in plane A. What is the converseof the statement “If lines m and n are parallel, thenlines m and n do not intersect”?a. If lines m and n are not parallel, then lines m

and n intersect.b. If lines m and n are not parallel, then lines m

and n do not intersectc. If lines m and n intersect, then lines m and n are

not parallel.d. If lines m and n do not intersect, then lines m

and n are parallel.

34. Given: ABC, BD bisects ABC, BD AC

Prove: AB CB

35. In the diagram of UVW below, A is the midpoint

of UV , B is the midpoint of UW , C is the midpoint

of VW , and AB and AC are drawn.

If VW 7x 3 and AB 3x 1, what is the length

of VC?a. 5b. 13c. 16d. 32

36. The lateral area of a right circular cone is equal to

120 cm2 . If the base of the cone has a diameterof 24 cm, what is the length of the slant height, incentimeters?a. 2.5b. 5c. 10d. 15.7

37. Line segment AB is a diameter of circle O whosecenter has coordinates (6,8). What are thecoordinates of point B if the coordinates of point Aare (4,2)?a. (1,3)b. (5,5)c. (8,14)d. (10,10)

Name: ________________________ ID: A

7

------------- Day 9 -------------------

38. In the diagram below, RCBT

and ABC areshown with mA 60 and mABT 125.

What is mACR?a. 125b. 115c. 65d. 55

39. In the diagram below, XYV TSV .

Which statement can not be proven?a. XVY TVSb. VYX VUT

c. XY TS

d. YV SV

40. If line is perpendicular to distinct planes P and Q,

then planes P and Qa. are parallelb. contain line c. are perpendiculard. intersect, but are not perpendicular

41. What is the equation of circle O shown in thediagram below?

a. (x 4)2 (y 1)2 3

b. (x 4)2 (y 1)2 3

c. (x 4)2 (y 1)2 9

d. (x 4)2 (y 1)2 9

42. In the diagram below, under which transformationis ABC the image of ABC?

a. D2

b. rx-axis

c. r y-axis

d. (x,y) (x 2,y)

Name: ________________________ ID: A

8

------------- Day 10 --------------

43. Triangle ABC has vertices A(6,6), B(9,0), andC(3,3). State and label the coordinates of

A' B' C', the image of ABC after a dilation ofD 1

3.

Answer:________________________

44. The diameter of a sphere is 5 inches. Determineand state the surface area of the sphere, to thenearest hundredth of a square inch .

Answer:___________________

45. The diagram below shows the construction of linem, parallel to line , through point P.

Which theorem was used to justify thisconstruction?a. If two lines are cut by a transversal and the

alternate interior angles are congruent, the linesare parallel.

b. If two lines are cut by a transversal and theinterior angles on the same side aresupplementary, the lines are parallel.

c. If two lines are perpendicular to the same line,they are parallel.

d. If two lines are cut by a transversal and thecorresponding angles are congruent, they areparallel.

46. The coordinates of the vertices of parallelogramSWAN are S(2,2), W(2,4), A(4,6), and N(0,8).State and label the coordinates of parallelogramS W AN , the image of SWAN after thetransformation T4,2 D 1

2. [The use of the set of

axes below is optional.]

Answer: __________________________________

47. In ABC, A B and C is an obtuse angle.Which statement is true?

a. AC AB and BC is the longest side.

b. AC BC and AB is the longest side.

c. AC AB and BC is the shortest side.

d. AC BC and AB is the shortest side.

Name: ________________________ ID: A

9

--------------- Day 11 ------------

48. Quadrilateral MATH has coordinates M(6,3),A(1,3), T(2,1), and H(4,1) . The image ofquadrilateral MATH after the compositionrx-axis T7,5 is quadrilateral M AT H . State and

label the coordinates of M AT H . [The use ofthe set of axes below is optional.]

49. A right circular cylinder has a height of 7 inchesand the base has a diameter of 6 inches. Determinethe lateral area, in square inches, of the cylinder interms of .

Answer: ___________________

50. A rectangular right prism is shown in the diagrambelow.

Which pair of edges are not coplanar?

a. BF and CG

b. BF and DH

c. EF and CD

d. EF and BC

51. In ABC, the measure of angle A is fifteen lessthan twice the measure of angle B. The measure ofangle C equals the sum of the measures of angle Aand angle B. Determine the measure of angle B.

Answer:_______________________

52. In the diagram below, circles A and B are tangent at

point C and AB is drawn. Sketch all commontangent lines.

Name: ________________________ ID: A

10

---------------- Day 12 -------------

53. In the diagram below, four pairs of triangles areshown. Congruent corresponding parts are labeledin each pair.

Using only the information given in the diagrams,which pair of triangles can not be provencongruent?a. Ab. Bc. Cd. D

54. In triangles ABC and DEF, AB 4, AC 5,DE 8, DF 10, and A D. Which methodcould be used to prove ABC DEF?a. AAb. SASc. SSSd. ASA

55. How many common tangent lines can be drawn tothe circles shown below?

a. 1b. 2c. 3d. 4

56. The coordinates of point P are (7,1). What are thecoordinates of the image of P after R90 about the

origin?a. (1,7)b. (7,1)c. (1,7)d. (1,7)

57. Triangle ABC is similar to triangle DEF. Thelengths of the sides of ABC are 5, 8, and 11.What is the length of the shortest side of DEF ifits perimeter is 60?a. 10b. 12.5c. 20d. 27.5

Name: ________________________ ID: A

11

--------- Day 13 ----------

58. Which graph represents a circle whose equation is

x 2 (y 1)2 9?

a.

b.

c.

d.

59. Chords AB and CD intersect at point E in a circlewith center at O. If AE 8, AB 20, and DE 16,

what is the length of CE?a. 6b. 9c. 10d. 12

60. Which quadrilateral does not always havecongruent diagonals?a. isosceles trapezoidb. rectanglec. rhombusd. square

61. Which diagram shows the construction of a 45°angle?

a.

b.

c.

d.

62. Points A(5,3) and B(7,6) lie on AB

. Points C(6,4)

and D(9,0) lie on CD

. Which statement is true?

a. AB

CD

b. AB

CD

c. AB

and CD

are the same line.

d. AB

and CD

intersect, but are notperpendicular.

Name: ________________________ ID: A

12

--------- Day 14 ----------

63. In ABC shown below, L is the midpoint of BC ,

M is the midpoint of AB, and N is the midpoint of

AC.

If MN 8, ML 5, and NL 6, the perimeter oftrapezoid BMNC isa. 35b. 31c. 28d. 26

64. Based on the construction below, which conclusionis not always true?

a. AB CDb. AB CDc. AE EBd. CE DE

65. The diagram below shows the construction of anequilateral triangle.

Which statement justifies this construction?a. A B C 180b. mA mB mCc. AB AC BCd. AB BC AC

66. Triangle ABC has vertices A(0,0), B(6,8), andC(8,4). Which equation represents the

perpendicular bisector of BC ?a. y 2x 6b. y 2x 4

c. y 12

x 52

d. y 12

x 192

67. Plane A and plane B are two distinct planes that areboth perpendicular to line . Which statementabout planes A and B is true?

a. Planes A and B have a common edge, whichforms a line.

b. Planes A and B are perpendicular to each

other.c. Planes A and B intersect each other at exactly

one point.d. Planes A and B are parallel to each other.

Name: ________________________ ID: A

13

--------- Day 15 ----------

68. As shown in the diagram below, a landscaper usesa cylindrical lawn roller on a lawn. The roller has aradius of 9 inches and a width of 42 inches.

To the nearest square inch, the area the rollercovers in one complete rotation isa. 2,374b. 2,375c. 10,682d. 10,688

69. Which equation represents circle A shown in thediagram below?

a. (x 4)2 (y 1)2 3

b. (x 4)2 (y 1)2 3

c. (x 4)2 (y 1)2 9

d. (x 4)2 (y 1)2 9

70. Triangle ABC has vertices at A(3,0), B(9,5), and

C(7,8). Find the length of AC in simplest radicalform.

Answer:__________________

71. A right circular cylinder with a height of 5 cm has abase with a diameter of 6 cm. Find the lateral areaof the cylinder to the nearest hundredth of a squarecentimeter.

Lateral Area = _________________

Find the volume of the cylinder to the nearesthundredth of a cubic centimeter.

Volume = _______________

72. A rectangular prism has a base with a length of 25,a width of 9, and a height of 12. A second prismhas a square base with a side of 15. If the volumesof the two prisms are equal, what is the height ofthe second prism?a. 6b. 8c. 12d. 15

Name: ________________________ ID: A

14

--------- Day 16 ----------

73. Triangle ABC has vertices A(5,1), B(1,4) andC(1,1). State and label the coordinates of thevertices of ABC , the image of ABC,following the composite transformation T1,1 D2 .

[The use of the set of axes below is optional.]

74. If distinct planes R and S are both perpendicular toline , which statement must always be true?a. Plane R is parallel to plane S.b. Plane R is perpendicular to plane S.c. Planes R and S and line are all parallel.

d. The intersection of planes R and S is

perpendicular to line .

75. How many points in the coordinate plane are 3units from the origin and also equidistant from boththe x-axis and the y-axis?a. 1b. 2c. 8d. 4

76. On the set of axes below, graph the locus of points4 units from (0,1) and the locus of points 3 unitsfrom the origin. Label with an X any points thatsatisfy both conditions.

77. As shown in the diagram below, a right pyramid

has a square base, ABCD, and EF is the slantheight.

Which statement is not true?

a. EA EC

b. EB EFc. AEB BECd. CED is isosceles

Name: ________________________ ID: A

15

--------- Day 17 ----------

78. Line passes through the point (5,3) and is parallelto line k whose equation is 5x y 6. An equationof line is

a. y 15

x 2

b. y 5x 28

c. y 15

x 2

d. y 5x 28

79. Given: ABD, BC is the perpendicular bisector of

AD

Which statement can not always be proven?

a. AC DC

b. BC CDc. ACB DCBd. ABC DBC

80. In the diagram of ABC below, AB is extended topoint D.

If mCAB x 40, mACB 3x 10,mCBD 6x , what is mCAB?a. 13b. 25c. 53d. 65

81. In the diagram of trapezoid ABCD below,

AB DC , AD BC , mA 4x 20, andmC 3x 15.

What is mD?a. 25b. 35c. 60d. 90

82. What is the equation for circle O shown in thegraph below?

a. (x 3)2 (y 1)2 6

b. (x 3)2 (y 1)2 6

c. (x 3)2 (y 1)2 9

d. (x 3)2 (y 1)2 9

83. If ABC JKL RST , then BC must becongruent to

a. JL

b. JK

c. ST

d. RS

Name: ________________________ ID: A

16

--------- Day 18 ----------

84. State whether the lines represented by the

equations y 12

x 1 and y 4 12

(x 2) are

parallel, perpendicular, or neither. Explain youranswer.

Answer:________________________

Why?__________________________________

85. The coordinates of two vertices of square ABCDare A(2,1) and B(4,4). Determine the slope of side

BC .

Answer:_______________

86. Which set of equations represents two circles thathave the same center?

a. x 2 (y 4)2 16 and (x 4)2 y 2 16

b. (x 3)2 (y 3)2 16 and

(x 3)2 (y 3)2 25

c. (x 7)2 (y 2)2 16 and

(x 7)2 (y 2)2 25

d. (x 2)2 (y 5)2 16 and

(x 2)2 (y 5)2 25

87. Trapezoid TRAP, with median MQ, is shown in thediagram below. Solve algebraically for x and y.

x = __________ y = __________

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

parallel to diameter AOB and mCD 110.

What is mDB ?a. 35b. 55c. 70d. 110

Name: ________________________ ID: A

17

--------- Day 19 ----------

89. As shown in the diagram of rectangle ABCD

below, diagonals AC and BD intersect at E.

If AE x 2 and BD 4x 16, then the length of

AC isa. 6b. 10c. 12d. 24

90. What are the coordinates of the center and thelength of the radius of the circle whose equation is

(x 1)2 (y 5)2 16?a. (1,5) and 16b. (1,5) and 16c. (1,5) and 4d. (1,5) and 4

91. When the system of equations y 2 (x 4)2 and2x y 6 0 is solved graphically, the solution isa. (4,2) and (2,2)b. (4,2) and (2,2)c. (4,2) and (6,6)d. (4,2) and (6,6)

92. After the transformation r y x, the image of ABC

is ABC . If AB 2x 13 and AB 9x 8,find the value of x.

Answer:_______________

93. Point A is on line m. How many distinct planeswill be perpendicular to line m and pass throughpoint A?a. oneb. twoc. zerod. infinite

94. Two intersecting lines are shown in the diagrambelow. Sketch the locus of points that areequidistant from the two lines. Sketch the locus ofpoints that are a given distance, d, from the point ofintersection of the given lines. State the number ofpoints that satisfy both conditions.

95. A student wrote the following equations:3y 6 2x

2y 3x 6The lines represented by these equations area. parallelb. the same linec. perpendiculard. intersecting, but not perpendicular

Name: ________________________ ID: A

18

--------- Day 20 ----------

96. Which equation represents the circle whose centeris (5,3) and that passes through the point (1,3)?

a. (x 1)2 (y 3)2 16

b. (x 1)2 (y 3)2 16

c. (x 5)2 (y 3)2 16

d. (x 5)2 (y 3)2 16

97. Determine, in degrees, the measure of each interiorangle of a regular octagon.

Answer:_____________________

98. In the diagram below of right triangle ABC, altitude

CD is drawn to hypotenuse AB.

If AD 3 and DB 12, what is the length of

altitude CD?a. 6

b. 6 5c. 3

d. 3 5

99. In the diagram below of quadrilateral ABCD, E and

F are points on AB and CD, respectively,

BE DF , and AE CF.

Which conclusion can be proven?

a. ED FB

b. AB CDc. A Cd. AED CFB

100. The endpoints of AB are A(3,4) and B(7,2).

Determine and state the length of AB in simplestradical form.

Answer:____________________________

101. What is the perimeter of a rhombus whosediagonals are 16 and 30?a. 92b. 68c. 60d. 17

Name: ________________________ ID: A

19

--------- Day 21 ----------

102. A circle has the equation (x 3)2 (y 4)2 10.Find the coordinates of the center of the circle andthe length of the circle's radius.

Center:________ radius = __________

103. In circle O, diameter AB intersects chord CD at E.If CE ED, then CEA is which type of angle?a. straightb. obtusec. acuted. right

104. Using a compass and straightedge, construct a lineperpendicular to line through point P. [Leave allconstruction marks.]

105. Which graph represents a circle whose equation is

x 2 (y 2)2 4?

a.

b.

c.

d.

106. In ABC, mA 3x 1, mB 4x 17, andmC 5x 20. Which type of triangle is ABC?a. rightb. scalenec. isoscelesd. equilateral

Name: ________________________ ID: A

20

------------- Day 22 -----------

107. Triangle ABC is shown in the diagram below.

If DE joins the midpoints of ADC and AEB, whichstatement is not true?

a. DE 12

CB

b. DE CB

c.ADDC DE

CBd. ABC AED

108. In circle O shown below, chords AB and CD and

radius OA are drawn, such that AB CD,

OE AB, OF CD, OF 16, CF y 10, andCD 4y 20.

Determine the length of DF . ______________

Determine the length of OA. ______________

109. For which measures of the sides of ABC is angleB the largest angle of the triangle?a. AB 2, BC 6, AC 7b. AB 6, BC 12, AC 8c. AB 16, BC 9, AC 10d. AB 18, BC 14, AC 5

110. The coordinates of the vertices of ABC areA(6,5), B(4,8), and C(1,6). State and label thecoordinates of the vertices of ABC , the imageof ABC after the composition of transformationsT(4,5) r y-axis . [The use of the set of axes below is

optional.]

111. Write an equation of a circle whose center is (3,2)and whose diameter is 10.

Answer:_________________________

Name: ________________________ ID: A

21

------------- Day 23 -----------

112. The midpoint of AB is M(4,2). If the coordinatesof A are (6,4), what are the coordinates of B?a. (1,3)b. (2,8)c. (5,1)d. (14,0)

113. Using a compass and straightedge, construct thebisector of MJH . [Leave all construction marks.]

114. If ABC and its image, ABC , are graphed ona set of axes, ABC ABC under eachtransformation excepta. D2

b. R90

c. r y x

d. T(2,3)

115. The diagram below shows rectangle ABCD with

points E and F on side AB. Segments CE and DFintersect at G, and ADG BCG. Prove:

AE BF

Statement Reason

Name: ________________________ ID: A

22

------------- Day 24 -----------

116. The diagram below shows ABD, with ABC

,

BE AD, and EBD CBD.

If mABE 52, what is mD?a. 26b. 38c. 52d. 64

117. As shown in the diagram below, CD is a median ofABC.

Which statement is always true?

a. AD DB

b. AC ADc. ACD CDBd. BCD ACD

118. A circle with the equation (x 6)2 (y 7)2 64does not include points in Quadranta. Ib. IIc. IIId. IV

119. In ABC, D is the midpoint of AB and E is the

midpoint of BC . If AC 3x 15 and DE 6, whatis the value of x?

a. 6b. 7c. 9d. 12

120. A tree, T, is 6 meters from a row of corn, c, asrepresented in the diagram below. A farmer wantsto place a scarecrow 2 meters from the row of cornand also 5 meters from the tree. Sketch both loci.Indicate, with an X, all possible locations for thescarecrow.

Name: ________________________ ID: A

23

------------- Day 25 -----------

121. Write an equation of the line that is theperpendicular bisector of the line segment havingendpoints (3,1) and (3,5). [The use of the gridbelow is optional]

Answer:__________________________

122. The equation of a circle is (x 2)2 (y 5)2 32.What are the coordinates of the center of this circleand the length of its radius?a. (2,5) and 16b. (2,5) and 16

c. (2,5) and 4 2

d. (2,5) and 4 2

123. In the diagram below, diameter AB bisects chord

CD at point E in circle F.

If AE 2 and FB 17, then the length of CE isa. 7b. 8c. 15d. 16

124. Find, in simplest radical form, the length of the linesegment with endpoints whose coordinates are(1,4) and (3,2).

Answer:______________________

125. Triangle ABC has the coordinates A(1,2), B(5,2),and C(5,5). Triangle ABC is rotated 180° about theorigin to form triangle A' B' C'. Triangle A' B' C' isa. acuteb. isoscelesc. obtused. right

Name: ________________________ ID: A

24

---------- Day 26 ------------

126. Using a compass and straightedge, construct the

perpendicular bisector of AB. [Leave allconstruction marks.]

127. In the diagram below of circle O, PAC and PBDare secants.

If mCD 70 and mAB 20, what is the degreemeasure of P?a. 25b. 35c. 45d. 50

128. Square ABCD has vertices A(2,3), B(4,1),C(2,5), and D(4,3). What is the length of a sideof the square?

a. 2 5

b. 2 10

c. 4 5

d. 10 2

129. In circle R shown below, diameter DE is

perpendicular to chord ST at point L.

Which statement is not always true?

a. SL TLb. RS DR

c. RL LEd. (DL)(LE) (SL)(LT)

130. On the set of axes below, graph the locus of points4 units from the x-axis and equidistant from thepoints whose coordinates are (2,0) and (8,0).Mark with an X all points that satisfy bothconditions.

Name: ________________________ ID: A

25

---------- Day 27 ------------

131. On the ray drawn below, using a compass andstraightedge, construct an equilateral triangle witha vertex at R. The length of a side of the trianglemust be equal to a length of the diagonal ofrectangle ABCD.

132. In the diagram of ABC below, medians AD and

BE intersect at point F.

If AF 6, what is the length of FD?a. 6b. 2c. 3d. 9

133. In the diagram below, AC and AD are tangent to

circle B at points C and D, respectively, and BC ,

BD , and BA are drawn.

If AC 12 and AB 15, what is the length of BD?a. 5.5b. 9c. 12d. 18

134. The volume of a sphere is approximately 44.6022cubic centimeters. What is the radius of the sphere,to the nearest tenth of a centimeter?a. 2.2b. 3.3c. 4.4d. 4.7

135. As shown in the diagram below, FD and CB

intersect at point A and ET is perpendicular to both

FD and CB at A.

Which statement is not true?

a. ET is perpendicular to plane BAD.

b. ET is perpendicular to plane FAB.

c. ET is perpendicular to plane CAD.

d. ET is perpendicular to plane BAT.

Name: ________________________ ID: A

26

---------- Day 28 ------------

136. The equation of a line is y 23

x 5. What is an

equation of the line that is perpendicular to thegiven line and that passes through the point (4,2)?

a. y 23

x 23

b. y 32

x 4

c. y 32

x 7

d. y 32

x 8

137. Circle O with AOC and ABC is shown in thediagram below.

What is the ratio of mAOC to mABC ?a. 1 : 1b. 2 : 1c. 3 : 1d. 1 : 2

138. How many points are 5 units from a line and alsoequidistant from two points on the line?a. 1b. 2c. 3d. 0

139. Lines p and q are intersected by line r, as shownbelow.

If m1 7x 36 and m2 5x 12, for whichvalue of x would p q?a. 17b. 24c. 83d. 97

140. Trapezoid QRST is graphed on the set of axesbelow.

Under which transformation will there be noinvariant points?a. r y 0

b. rx 0

c. r (0,0)

d. r y x

Name: ________________________ ID: A

27

---------- Day 29 ------------

141. What is the slope of the line perpendicular to theline represented by the equation 2x 4y 12?a. 2b. 2

c. 12

d.12

142. As shown in the diagram below, when righttriangle DAB is reflected over the x-axis, its imageis triangle DCB.

Which statement justifies why AB CB?a. Distance is preserved under reflection.b. Orientation is preserved under reflection.c. Points on the line of reflection remain

invariant.d. Right angles remain congruent under

reflection.

143. In a coordinate plane, the locus of points 5 unitsfrom the x-axis is thea. lines x 5 and x 5b. lines y 5 and y 5c. line x 5, onlyd. line y 5, only

144. In right triangle ABC below, CD is the altitude to

hypotenuse AB. If CD 6 and the ratio of AD to

AB is 1:5, determine and state the length of BD .[Only an algebraic solution can receive full credit.]

145. If RST ABC , mA x 2 8x , mC 4x 5,and mR 5x 30, find mC . [Only an algebraicsolution can receive full credit.]

Answer: ________________________

146. The measure of an interior angle of a regularpolygon is 120°. How many sides does the polygonhave?a. 5b. 6c. 3d. 4

Name: ________________________ ID: A

28

---------- Day 30 ------------

147. The sides of a triangle are 8, 12, and 15. Thelongest side of a similar triangle is 18. What is theratio of the perimeter of the smaller triangle to theperimeter of the larger triangle?a. 2:3b. 4:9c. 5:6d. 25:36

148. The bases of a right triangular prism are ABCand DEF. Angles A and D are right angles,AB 6, AC 8, and AD 12. What is the length

of edge BE?a. 10b. 12c. 14d. 16

149. Consider the relationship between the twostatements below.

If 16 9 4 3, then 5 4 3

If 16 9 4 3, then 5 4 3These statements area. inversesb. conversesc. contrapositivesd. biconditionals

150. What is the difference between the sum of themeasures of the interior angles of a regularpentagon and the sum of the measures of theexterior angles of a regular pentagon?a. 36b. 72c. 108d. 180

151. In the diagram of BCD shown below, BA is

drawn from vertex B to point A on DC , such that

BC BA.

In DAB, mD x , mDAB 5x 30, andmDBA 3x 60. In ABC, AB 6y 8 andBC 4y 2. [Only algebraic solutions can receivefull credit.]

Find mD. __________________

Find mBAC . _________________

Find the length of BC . _________________

Find the length of DC ._________________