Geometry Regents Review

Transcription

1 Name: ate: 1. set of points that extend indefinitely in two opposite directions is called. 5. What is the image of (5, 1) under a counterclockwise rotation of 90?. a line. an angle. a plane. a ray. (1, 5). (1, 5). (1, 5). (0, 0) 2. Two non-parallel lines intersect at a.. point. line. plane. none of these 3. Which of the following sets of points are collinear?.,,.,,.,,.,, 4. What is the image of point after a rotation of 90 in the clockwise direction? 6. Find the coordinates of P, the image of P(2, 1) after a clockwise rotation of 180 about the origin.. (2, 1). (2, 1). (1, 2). (1, 2) 7. Select the letters that would appear the same after a 180 rotation about the center. I. II. H III. R IV. S. I only. II only. III only. II and IV G E F H... E. F page 1

2 8. is the image of. Which of the following rotations could be used to perform this transformation? 12. In the diagram, K and K are congruent. I. 90 clockwise II. 90 counterclockwise III. 270 clockwise IV. 270 counterclockwise Which of the following is a way of transforming K into K?. a rotation of 180 about the origin. II only. II and III. III only. II and IV 9. point (3, 5) is reflected over the x-axis. What are the coordinates of the image point?. a clockwise rotation of 90 about the point (0, 2). a reflection across the x-axis, then a translation down 2 units. a reflection across the y-axis, then a reflection across the line y = 2. (3, 0). (3, 5). (5, 3). (3, 5) 10. Find Q, the image of Q(2, 3), after a reflection across the line y = x. 13. Which of the following is not a congruence transformation for a two-dimensional figure?. dilation. rotation. reflection. translation. (2, 3). (2, 3). (3, 2). (3, 2) 11. What is the the rotational symmetry of a rhombus? State the congruence relation for XYZ and PQR.. S.. SS. not necessarily congruent page 2

3 15. State the congruence relation for and EF.. SSS 17. The orresponding ngles onjecture states that if two parallel lines are cut by a transversal, the corresponding angles are congruent. The picture below shows this relationship.. SS. S. SS 16. The S congruency axiom states that two triangles are congruent if: Which of these congruent angles are corresponding angles?. two angles and the contained side of one triangle are equal to two angles and the contained angle of the other triangle.. two sides and the contained angle of one triangle are equal to two sides and the contained angle of the other triangle.. two angles and a side of one triangle are equal to two angles and a side of the other triangle.. two sides and the excluded angle of one triangle are equal to two sides and the excluded angle of the other triangle.. 1 and 4. 1 and 3. 4 and 8. 4 and The perpendicular bisector of a line segment will result in angles that are.. acute. obtuse. right. complementary page 3

4 19. In hexagon RGON the diagonals RO and N bisect each other. Jared s geometry class is writing a proof to show that R = ON. Statement 1. RO bisects N, N bisects RO 2. RS = SO, S = SN 3. OSN = SR given 4. NOS = RS 4. SS 5. R = ON 5. PT Reason 2. efinition of segment bisector The teacher asks Jared to justify step three. What should he answer?. djacent angles are congruent.. Vertical angles are congruent.. lternate Interior angles are congruent.. efinition of angle bisector. 20. Given: Prove: = 3 = 4 statement 1. = 1. reason page 4

5 21. Given: LF = KF L = K Prove: LJ = KJ statement reason 22. Given: WY is the angle bisector of XWZ m XYW = m ZYW 23. Given: WY is the angle bisector of XWZ m XYW = m ZYW Prove: WXY = WZY 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)?. definition of an altitude. sides opposite equal s are equal. reflexive property. definition of a right angle 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 (1)?. given. definition of an altitude. definition of angle bisector. definition of a perpendicular page 5

6 24. Given: VX is a median of VWY WZ = YZ 25. Given: VT bisects RW RW bisects TV Prove: WXZ = YXZ Prove: RSV = WST 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) In the above proof, what is reason (2)?. definition of median. definition of midpoint 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)?.. S. SS. SSS. definition of perpendicular bisector. given page 6

7 26. Given: Prove: = m = m 27. Given: Prove: is the median to E E is the median to E Statement Reason (1) = (2) m = m (3) = (4) = (5) m = m (6) In the above proof, what is reason (6)?. PT. SSS. vertical angles. alternate interior angles statement 1. is the median to E 2. = E 3. m 1 = m 2 4. E is the median to 5. = 6. = E 7. m 3 = m 4 8. E reason In the proof, what is the reason for line 7?. alternate interior angles are congruent. definition of parallel. isosceles triangle theorem. PT 28. In the proof, what is the reason for line 3?. alternate interior angles are congruent. vertical angles are congruent. corresponding angles are congruent. definition of a median page 7

8 29. Given: Prove: is the perpendicular bisector of is isosceles Statement 1. is bisector of given Reason 2. def n of bisector 3. def n of bisector 4. = 5. = SS 6. = 7. is isosceles What is the reason for step 7?. m = m. definition of isosceles ( = ). angles opposite = sides are =. sides opposite = angles are = 30. Hazel says, ll isosceles triangles are congruent. mir says, ll isosceles triangles are similar. Who is correct? Explain your reasoning. page 8

9 31. omplete the following proof. Given: Prove: = is the midpoint of E is the midpoint of E = statement reason 1. = given 2. = 2 1 () defn. of midpoint 3. E = 2 1 () defn. of midpoint 4. both 1 2 of equal lengths 5. m = m E = 32. Fill in the missing statements and reasons for the following proof. Given: Prove: = M is the angle bisector of 1 = 2 statement 1. given reason 2. P = P 3. P = P 4. reflective property 5. 1 = 2 page 9

10 33. Given: Prove: E F m E = m F Statements Reasons 34. Given: m = m = Prove: bisects Statements Reasons page 10

11 35. Given: =, bisects Prove: m = 90 Statements Reasons 36. Given: Prove: E is the perpendicular bisector of, m FE = m E, F = F = Statements Reasons page 11

12 37. Given: =, m 1 = m 2 Prove: = E Statements Reasons 38. Given: m = m M = N Prove: M = N Statements Reasons page 12

13 39. Given: Prove: is the median to E, E is the median to. E Statements Reasons 40. Given: is equilateral, EF is equilateral. Prove: F = E Statements Reasons 41. RHOM is a rhombus.,,, and are the midpoints of each side. Prove that is a rectangle. 42. In the figure, TU QR. Which proportion is not true?.. QR RS = TU US QR QS = TU TS.. RU QR = US TU ST TU = SQ QR page 13

14 43. How many similar triangles are in the diagram? cannot be determined 47. Which of the following ratios is the tangent of an angle?. opposite hypotenuse. hypotenuse adjacent. adjacent hypotenuse. opposite adjacent 44. In the diagram,, E, E = 17, E = 8, and = 32. Find E Given the triangle shown, which of the following is true?. sin = c b. cos = c b. tan = b a. sin = b c 45. In the figure, RS = 6, RT = 4, and TU = 10. What is the length of UV? not enough information 49. Which of the following statements is incorrect for XYZ?. sin Z = tan Y = XZ = 13. cos X = In the triangle below, sin P = Find cos R. etermine the length of ST if MN is (8x 3) units.. 4x x 6. 4x x Find the length of side x page 14

15 52. In, = 10, = 8, m = 90 and m = 90. How long is? 53. In triangle PQR, PQ = 8 cm, QR = 6 cm, and m PQR = 30. Exactly how long is PR? Given: Prove: QR and QS are tangents to the circle centered at P. QP intersects the circle at M. 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: Prove: is a parallelogram F = statement reason 1. Given 2. m = m 3. m F = m 4. both = m 5. page 15

16 56. Given: Prove: OU bisects RP m OTR = 90 TO OU statement reason 1. Given 2. Given 3. OU PR 4. m OUR = m TOU = In the circle shown, chords and intersect at E. If E = x 4, E = 2x + 9, E = x, and E = x + 6. How long is? Given the circle with center O and with m ROQ = 160, find the measure of minor arc PR. ( Find the value of x If m NOM = 60, then what is the length of the minor arc NM? (. π 4. π. 3π 2. 2π 59. What is the measure, in degrees, of? page 16

17 62. If r = 12 cm, what is the area of this sector? Express your answer to the nearest tenth of a centimeter cm cm cm cm What is the equation of the line perpendicular to the line shown in the diagram that passes through the point (2, 4)?. x + 3y = 14. x 3y = 10. 3x y = 2. 2x + 3y = Write the equation for the circle. 67. Join on the coordinate plane. etermine the midpoint of.. (x 3) 2 + (y 1) 2 = 9. (x 3) 2 + (y + 1) 2 = 3. (x 3) 2 + (y + 1) 2 = 3. (x 3) 2 + (y + 1) 2 = What is the equation of a circle having radius 5 and center (3, 2)?. (x + 3) 2 + (y 2) 2 = 5. (x + 3) 2 + (y 2) 2 = 25. (x 3) 2 + (y + 2) 2 = 5. (1, 1). (1, 0). (1, 0). (1, 1) 68. One endpoint of a line segment is at (1, 2). The midpoint of the line segment is at (5, 8). etermine the coordinate of the other endpoint.. (3, 4). (3.5, 5). (6, 10). (9, 14) 65.. (x 3) 2 + (y + 2) 2 = 25 is the diameter of a circle where is (2, 0) and is (10, 8). What is the equation of the circle? 69. Given the coordinates of X, Y, and Z, as shown in the figure, find the perimeter of the triangle. 6 units. 11 units. 12 units. 14 units page 17

18 70. The formula for area of a triangle is = 1 2 bh. What is the area of the figure shown? 73. arli created a sculpture as shown in the diagram. The sculpture is 8 centimeters tall and the area of the bottom of the sculpture is 49 square inches. Which expression can be used to find how much clay arli used to make the sculpture? square units. 16 square units 74. What is the 3-dimensional figure shown?. 40 square units. 20 square units Top View Side View 71. What is a reasonable estimate for the area of one of the circles?. cylinder. cone. triangular pyramid. triangular prism. less than 5 cm 2. about 10 cm 2. about 20 cm 2. more than 35 cm ased on the diagram below, what is a reasonable estimate for the area of the shaded region?. less than 4 units 2. less than 6 units 2. less than 7 units 2. less than 8 units 2 page 18

19 75. Here is a picture of a 90 arc joined to a segment. The segment is the radius of the arc. 77. Parallelogram HN is drawn below with diagonals HN and intersecting at S. Suppose points and are fixed, but arc can rotate in space around segment. If the angle between the arc and the segment does not change, what 3-dimensional shape is created by the rotating arc?. a spiral. a cone. a cylinder. a hemisphere 76. In the diagram below, a sequence of rigid motions maps onto JKLM. Which statement is always true?. HN = 1 2. S = 1 2. HS = NS. HS = NS 78. The graph below shows two congruent triangle, and. If m = 82, m = 104, and m L = 121, the measure of M is Which rigid motion would map onto?. a rotation of 90 degrees counterclockwise about the origin. a translation of three units to the left and three units up. a rotation of 180 degrees about the origin. a reflection over the line y = x page 19

20 79. man was parasailing above a lake at an angle of elevation of 32 from a boat, as modeled in the diagram below. 81. In the diagram below, has endpoints with coordinates (5, 2) and (4, 10). If meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man? right hexagonal prism is shown below. two-dimensional cross section that is perpendicular to the base is taken from the prism. If is a point on and : = 1 : 2, what are the coordinates of?. (2, 2). ( 1 2, 4). (0, 14 3 ). (1, 6) Which figure describes the two-dimensional cross section?. triangle. rectangle. pentagon. hexagon 82. n ice cream waffle cone can be modeled by a right circular cone with a base diameter of 6.6 centimeters and a volume of 54.45π cubic centimeters. What is the number of centimeters in the height of the waffle cone? The vertices of PQR have coordinates P(2, 3), Q(3, 8), and R(7, 3). Under which transformation of PQR are distance and angle measure preserved?. (x, y) (2x, 3y). (x, y) (x + 2, 3y). (x, y) (2x, y + 3). (x, y) (x + 2, y + 3) page 20

21 84. In shown below, side is extended to point with m = (180 3x), m = (6x 40), and m = (x + 20). 87. The equation of a circle is x 2 + y 2 6x + 2y = 6. What are the coordinates of the center and the length of the radius of the circle?. center (3, 1) and radius 4. center (3, 1) and radius 4 What is m? ircle O is centered at the origin. In the diagram below, a quarter of circle O is graphed.. center (3, 1) and radius 16. center (3, 1) and radius In the diagram of below, E is parallel to, = 15, = 9, and = 40. The length of E is Which three-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?. cone. sphere. cylinder. hemisphere 86. Rectangle is the image of rectangle after a dilation centered at point by a scale factor of 3 2. Which statement is correct?. Rectangle has a perimeter that is 2 3 the perimeter of rectangle. 89. The line whose equation is 3x 5y = 4 is dilated by a scale factor of 3 5 centered at the origin. Which statement is correct?. The image of the line has the same slope as the pre-image but a different y-intercept.. The image of the line has the same y-intercept as the pre-image but a different slope.. The image of the line has the same slope and the same y-intercept as the pre-image.. The image of the line has a different slope and a different y-intercept from the pre-image.. Rectangle has a perimeter that is 3 2 the perimeter of rectangle.. Rectangle has an area that is the 2 3 area of rectangle.. Rectangle has an area that is the 3 2 area of rectangle. page 21

22 90. Which transformation would not carry a square onto itself?. a reflection over one of its diagonals 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 90 rotation clockwise about its center. a 180 rotation about one of its vertices. a reflection over the perpendicular bisector of one side 91. In circle M below, diameter, chords and, and radius M are drawn. Which statement is always true?. (XY)(SR) = (XZ)(RZ). XYZ = SRZ. XS = YR. XY SR = YZ RZ Which statement is not true?. is a right triangle. 93. s shown in the diagram below, EFG and F = EF. M is isosceles.. m = m M (. m = 2 1m ( If m F = 42.5, then m EF is parallelogram must be a rhombus if its diagonals. are congruent. bisect each other. do not bisect its angles. are perpendicular to each other page 22

23 95. What is an equation of a line which passes through (6, 9) and is perpendicular to the line whose equation is 4x 6y = 15? 99. In the diagram below, two concentric circles with center O, and radii O, O, OE, and OF are drawn.. y 9 = 3 2 (x 6). y 9 = 3 2 (x 6). y + 9 = 2 3(x + 6). y + 9 = 3 2 (x + 6) 96. Quadrilateral is inscribed in circle O, as shown below. If O = 4 and OE = 6, which relationship between the length of arc EF and the length of arc is always true? If m = 80, m = 75, m = (y + 30), and m = (x 10), which statement is true?. x = 85 and y = 50. x = 90 and y = 45. x = 110 and y = 75. x = 115 and y = regular pyramid has a square base. The perimeter of the base is 36 inches and the height of the pyramid is 15 inches. What is the volume of the pyramid in cubic inches?. The length of arc EF is 2 units longer than the length of arc.. The length of arc EF is 4 units longer than the length of arc.. The length of arc EF is 1.5 times the length of arc.. The length of arc EF is 2.0 times the length of arc Given: Parallelogram with diagonal drawn In the diagram below of, is a right angle, = 12, = 8, and altitude is drawn. Prove: = What is the length of page 23

24 101. The diagram below shows circle O with diameter. Using a compass and straightedge, construct a square that is inscribed in circle O. [Leave all construction marks.] 105. In the graph below, has coordinates (9, 2), (6, 6), and (3, 2), and RST has coordinates R(2, 9), S(5, 6), and T(2, 3) Given: Right triangle with right angle at If sin increases, does cos increase or decrease? Explain why In the diagram below, the circle has a radius of 25 inches. The area of the unshaded sector is 500π in 2. Is congruent to RST? Use the properties of rigid motions to explain your reasoning ob places an 18-foot ladder 6 feet from the base of his house and leans it up against the side of his house. Find, to the nearest degree, the measure of the angle the bottom of the ladder makes with the ground. etermine and state the degree measure of angle Q, the central angle of the shaded sector machinist creates a solid steel part for a wind turbine engine. The part has a volume of 1015 cubic centimeters. Steel can be purchased for $0.29 per kilogram, and has a density of 7.95 g/cm 3. If the machinist makes 500 of these parts, what is the cost of the steel, to the nearest dollar? page 24

25 107. Triangle and triangle E are graphed on the set of axes below s shown in the diagram below, an island (I) is due north of a marina (M). boat house (H) is 4.5 miles due west of the marina. From the boat house, the island is located at an angle of 54 from the marina. escribe a transformation that maps triangle onto triangle E. Explain why this transformation makes triangle E similar to triangle storage tank is in the shape of a cylinder with a hemisphere on the top. The highest point on the inside of the storage tank is 13 meters above the floor of the storage tank, and the diameter inside the cylinder is 8 meters. etermine and state, to the nearest cubic meter, the total volume inside the storage tank. etermine and state, to the nearest tenth of a mile, the distance from the boat house (H) to the island (I). etermine and state, to the nearest tenth of a mile, the distance from the island (I) to the marina (M) In the coordinate plane, the vertices of triangle PT are P(1, 6), (4, 5), and T(5, 2). Prove that PT is an isosceles triangle. State the coordinates of R so that quadrilateral PRT is a parallelogram. Prove that quadrilateral PRT is a parallelogram. page 25

26 111. two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what can not be the three-dimensional object? 115. In the diagram below, intersects E at, and E.. cone. cylinder. pyramid. rectangular prism 112. The image of EF is E F. Under which transformation will the triangles not be congruent?. a reflection through the origin. a reflection over the line y = x. a dilation with a scale factor of 1 centered at (2, 3). dilation with a scale factor of 2 3 centered at the origin If = 6.6 cm, E = 3.4 cm, E = 4.2 cm, and = 5.25 cm, what is the length of, to the nearest hundredth of a centimeter? s shown in the graph below, the quadrilateral is a rectangle The vertices of square RSTV have coordinates R(1, 5), S(3, 1), T(7, 3), and V(5, 7). What is the perimeter of RSTV? In the diagram below of circle O, chord is parallel to diameter O and m = 130. ( Which transformation would not map the rectangle onto itself?. a reflection over the x-axis. a reflection over the line x = 4 What is m? ( a rotation of 180 about the origin. a rotation of 180 about the point (4, 0) page 26

27 117. In the diagram below, triangle has points and E on sides and, respectively, such that E, = 1, = 3.5, and = Given with m = 62 and side extended to, as shown below. What is the length of E, to the nearest tenth? Which value of x makes =? 118. In the diagram below of parallelogram ROK, m is 70 and m ROS is In the diagram shown below, P is tangent to circle T at, and secant P is drawn where point is on circle T. What is m KSO? In the diagram below, GRS = RT, GR = 36, SR = 45, R = 15, and RT = 18. If P = 3 and = 15, what is the length of P? Which triangle similarity statement is correct? 123. rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously rotated around a straight line to form an object whose volume is 150π.. GRS RT by.. GRS RT by SS.. GRS RT by SSS.. GRS is not similar to RT The line represented by the equation 4y = 3x + 7 is transformed by a dilation centered at the origin. Which linear equation could represent its image?. 3x 4y = 9. 3x + 4y = 9. 4x 3y = 9. 4x + 3y = 9 Which line could the rectangle be rotated around?. a long side. a short side. the vertical line of symmetry. the horizontal line of symmetry page 27

28 124. If is a parallelogram, which statement would prove that is a rhombus?. =... = 128. Kirstie is testing values that would make triangle KLM a right triangle when LN is an altitude, and KM = 16, as shown below To build a handicapped-access ramp, the building code states that for every 1 inch of vertical rise in height, the ramp must extend out 12 inches horizontally, as shown in the diagram below. Which lengths would make triangle KLM a right triangle? What is the angle of inclination, x, of this ramp, to the nearest hundredth of a degree? In the diagram below of,, E, and F are the midpoints of,, and, respectively.. LM = 13 and KN = 6. LM = 12 and NM = 9. KL = 11 and KN = 7. LN = 8 and NM = In right triangle, m = 32, m = 90, and = 6.2 cm. What is the length of, to the nearest tenth of a centimeter? What is the ratio of the area of FE to the area of?. 1 : 1. 1 : 2. 1 : 3. 1 : The coordinates of the endpoints of are (8, 2) and (16, 6). Point P is on. What are the coordinates of point P, such that P : P is 3 : 5?. (1, 1). (7, 3). (9.6, 3.6). (6.4, 2.8) 130. The 2010 U.S. ensus populations and population densities are shown in the table below. State ( ) people Population ensity mi 2 Population in 2010 Florida ,801,310 Illinois ,830,632 New York ,378,102 Pennsylvania ,702,379 ased on the table above, which list has the states areas, in square miles, in order from largest to smallest?. Illinois, Florida, New York, Pennsylvania. New York, Florida, Illinois, Pennsylvania. New York, Florida, Pennsylvania, Illinois. Pennsylvania, New York, Florida, Illinois page 28

29 131. In a right triangle, sin (40 x) = cos (3x). What is the value of x? 135. Sue believes that the two cylinders shown in the diagram below have equal volumes regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be In a circle with a diameter of 32, the area of a sector is 512π. The measure of the angle of the 3 sector, in radians, is π 4π 16π 64π What is an equation of the perpendicular bisector of the line segment shown in the diagram below? Is Sue correct? Explain why In the diagram of rhombus PQRS below, the diagonals PR and QS intersect at point T, PR = 16, and QS = 30. etermine and state the perimeter of PQRS.. y + 2x = 0. y 2x = 0. 2y + x = 0. 2y x = 0 page 29

30 137. Quadrilateral MTH and its image M T H are graphed on the set of axes below The coordinates of the endpoints of are (2, 3) and (5, 1). etermine the length of, the image of, after a dilation of 1 2 centered at the origin. escribe a sequence of transformations that maps quadrilateral MTH onto quadrilateral M T H Using a compass and straightedge, construct a regular hexagon inscribed in circle O. [Leave all construction marks.] 140. In the diagram below of and XYZ, a sequence of rigid motions maps onto X, onto Z, and onto XZ. etermine and state whether = YZ. Explain why etermine and state the coordinates of the center and the length of the radius of a circle whose equation is x 2 + y 2 6x = 56 8y. page 30

31 142. Triangle PQR has vertices P(3, 1), Q(1, 7), and R(3, 3), and points and are midpoints of PQ and RQ, respectively. Use coordinate geometry to prove that is parallel to PR and is half the length of PR Keira has a square poster that she is framing and placing on her wall. The poster has a diagonal 58 cm long and fits exactly inside the frame. The width of the frame around the picture is 4 cm. etermine and state the total area of the poster and frame to the nearest tenth of a square centimeter In the diagram below of circle O, tangent E is drawn to diameter. hord is parallel to secant E, and chord is drawn Isosceles trapezoid has bases and with nonparallel legs and. Segments E, E, E, and E are drawn in trapezoid such that E = E, E E, and E E. Prove E = E and prove E is an isosceles triangle. Prove: = E page 31

32 146. rectangular in-ground pool is modeled by the prism below. The inside of the pool is 16 feet wide and 35 feet long. The pool has a shallow end and a deep end, with a sloped floor connecting the two ends. Without water, the shallow end is 9 feet long and 4.5 feet deep, and the deep end of the pool is 12.5 feet long In the diagram below, = EF. a) If the sloped floor has an angle of depression of 16.5 degrees, what is the depth of the pool at the deep end, to the nearest tenth of a foot? b) Find the volume of the inside of the pool to the nearest cubic foot. c) garden hose is used to fill the pool. Water comes out of the hose at a rate of 10.5 gallons per minute. How much time, to the nearest hour, will it take to fill the pool 6 inches from the top? [1 ft 3 = 7.48 gallons] Which sequence of transformations maps onto EF?. a reflection over the x-axis followed by a translation. a reflection over the y-axis followed by a translation. a rotation of 180 about the origin followed by a translation. a counterclockwise rotation of 90 about the origin followed by a translation page 32

33 148. On the set of axes below, the vertices of PQR have coordinates P(6, 7), Q(2, 1), and R(1, 3) Given MRO shown below, with trapezoid PTRO, MR = 9, MP = 2, and PO = 4. What is the length of TR? What is the area of PQR? line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true? 149. In right triangle, m = 90. If cos = 5 13, which function also equals 5 13?. tan. tan. sin. sin ( 150. In the diagram below, m = The line segments are perpendicular, and the image is one-half of the length of the given line segment.. The line segments are perpendicular, and the image is twice the length of the given line segment.. The line segments are parallel, and the image is twice the length of the given line segment.. The line segments are parallel, and the image is one-half of the length of the given line segment Which figure always has exactly four lines of reflection that map the figure onto itself?. square. rectangle What is the number of degrees in the measure of?. regular octagon. equilateral triangle page 33

34 154. In the diagram below of circle O, chord F bisects chord at E In the diagram below, E divides and proportionally, m = 26, m = 82, and F bisects E. If = 12 and FE is 5 more than E, then FE is Kelly is completing a proof based on the figure below. The measure of angle F is Which set of statements would describe a parallelogram that can always be classified as a rhombus? I. iagonals are perpendicular bisectors of each other. II. iagonals bisect the angles from which they are drawn. III. iagonals form four congruent isosceles right triangles. She was given that = EF, and has already proven = E. Which pair of corresponding parts and triangle congruency method would not prove = EF?. I and II. I and III. II and III. I, II, and III.. = F and SS = EF and SS 158. The equation of a circle is x 2 + y 2 12y + 20 = 0. What are the coordinates of the center and the length of the radius of the circle?. = F and S. = FE and S. center (0, 6) and radius 4. center (0, 6) and radius 4. center (0, 6) and radius 16. center (0, 6) and radius 16 page 34

35 159. In the diagram of RST below, m T = 90, RS = 65, and ST = The pyramid shown below has a square base, a height of 7, and a volume of 84. What is the measure of S, to the nearest degree? Triangle is the image of after a dilation followed by a translation. Which statement(s) would always be true with respect to this sequence of transformations? I. = II. III. IV. = What is the length of the side of the base? In the diagram below of triangle MNO, M and O are bisected by MS and OR, respectively. Segments MS and OR intersect at T, and m N = 40.. II, only. I and II. II and III. II, III, and IV 161. Line segment RW has endpoints R(4, 5) and W(6, 20). Point P is on RW such that RP : PW is 2 : 3. What are the coordinates of point P?. (2, 9). (0, 11). (2, 14). (10, 2) If m TMR = 28, the measure of angle OTS is In the diagram below, right triangle has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around?. 32π. 48π. 96π. 144π page 35

36 165. What is an equation of a line that is perpendicular to the line whose equation is 2y = 3x 10 and passes through (6, 1)?. y = 2 3 x 5. y = 2 3 x fabricator is hired to make a 27-foot-long solid metal railing for the stairs at the local library. The railing is modeled by the diagram below. The railing is 2.5 inches high and 2.5 inches wide and is comprised of a rectangular prism and a half-cylinder.. y = 2 3 x + 1. y = 2 3 x In quadrilateral LUE shown below, E = UL. How much metal, to the nearest cubic inch, will the railing contain? Which information would be sufficient to prove quadrilateral LUE is a parallelogram? L EU. LU E E = L. LU = EU 170. In the diagram below, = 7.2 and E = 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 the building does the ladder touch the building? In the two distinct acute triangles and EF, = E. Triangles and EF are congruent when there is a sequence of rigid motions that maps. onto, and onto F. onto F, and onto EF. onto F, and onto EF. point onto point, and onto E Which statement is not sufficient to prove E?. E. E = 2.7 and = 8.1. = 3.6 and = E = 3.0, = 9.0, = 2.9, and = Given: Trapezoid JKLM with JK ML. Using a compass and straightedge, construct the altitude from vertex J to ML. page 36

37 172. etermine and state, in terms of π, the area of a sector that intercepts a 40 arc of a circle with a radius of Triangle and triangle EF are drawn below The diagram below shows two figures. Figure is a right triangular prism and figure is an oblique triangular prism. The base of figure has a height of 5 and a length of 8 and the height of prism is 14. The base of figure has a height of 8 and a length of 5 and the height of prism is 14. Figure Figure If = E, = F, and =, write a sequence of transformations that maps triangle onto triangle EF Line n is represented by the equation 3x + 4y = 20. etermine and state the equation of line p, the image of line n, after a dilation of scale factor 1 3 centered at the point (4, 2). Explain your answer. Use avalieri s Principle to explain why the volumes of these two triangular prisms are equal When volleyballs are purchased, they are not fully inflated. partially inflated volleyball can be modeled by a sphere whose volume is approximately 180 in 3. fter being fully inflated, its volume is approximately 294 in 3. To the nearest tenth of an inch, how much does the radius increase when the volleyball is fully inflated? 175. In right triangle shown below, altitude is drawn to hypotenuse. Explain why. page 37

38 178. Triangle has vertices at (5, 2), (4, 7), and (2, 7), and triangle EF has vertices at (3, 2), E(2, 7), and F(0, 7). Graph and label and EF on the set of axes below. etermine and state the single transformation where EF is the image of. Use your transformation to explain why = EF Given: Prove: RS and TV bisect each other at point X TR and SV are drawn TR SV 180. gas station has a cylindrical fueling tank that holds the gasoline for its pumps, as modeled below. The tank holds a maximum of 20,000 gallons of gasoline and has a length of 34.5 feet. metal pole is used to measure how much gas is in the tank. To the nearest tenth of a foot, how long does the pole need to be in order to reach the bottom of the tank and still extend one foot outside the tank? Justify your answer. [1 ft 3 = 7.48 gallons] page 38

39 181. 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 student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation? Freda, who is training to use a radar system, detects an airplane flying at a constant speed and heading in a straight line to pass directly over her location. She sees the airplane at an angle of elevation of 15 and notes that it is maintaining a constant altitude of 6250 feet. One minute later, she sees the airplane at an angle of elevation of 52. How far has the airplane traveled, to the nearest foot? etermine and state the speed of the airplane, to the nearest mile per hour three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?. 9 inches. 2 inches. 15 inches. 18 inches 185. Kevin s work for deriving the equation of a circle is shown below. x 2 + 4x = (y 2 20) STEP 1 x 2 + 4x = y STEP 2 x 2 + 4x + 4 = y STEP 3 (x + 2) 2 = y STEP 4 (x + 2) 2 + y 2 = 16 In which step did he make an error in his work?. Step 1. Step 2. Step 3. Step 4 page 39

40 186. Which transformation of O would result in an image parallel to O? 188. company is creating an object from a wooden cube with an edge length of 8.5 cm. right circular cone with a diameter of 8 cm and an altitude of 8 cm will be cut out of the cube. Which expression represents the volume of the remaining wood?. (8.5) 3 π(8) 2 (8). (8.5) 3 π(4) 2 (8). (8.5) π(8)2 (8). (8.5) π(4)2 (8) 189. Two right triangles must be congruent if. a translation of two units down. a reflection over the x-axis. a reflection over the y-axis. a clockwise rotation of 90 about the origin 187. Using the information given below, which set of triangles can not be proven similar?. an acute angle in each triangle is congruent. the lengths of the hypotenuses are equal. the corresponding legs are congruent. the areas are equal 190. Which sequence of transformations will map onto?.... reflection and translation. rotation and reflection. translation and dilation.. dilation and rotation page 40

41 191. In parallelogram, diagonals and intersect at E. Which statement does not prove parallelogram is a rhombus? 195. In RST shown below, altitude SU is drawn to RT at U... =.. = bisects In the diagram below of circle O, O and O are radii, and chords,, and are drawn. If SU = h, UT = 12, and RT = 42, which value of h will make RST a right triangle with RST as a right angle? In the diagram below, has vertices (4, 5), (2, 1), and (7, 3). Which statement must always be true?. = O. m = 1 2 m O. and O are isosceles.. The area of is twice the area of O foot support post leans against a wall, making a 70 angle with the ground. To the nearest tenth of a foot, how far up the wall will the support post reach? Line segment NY has endpoints N(11, 5) and Y(5, 7). What is the equation of the perpendicular bisector of NY? What is the slope of the altitude drawn from to? In the diagram below, ERM JTM.. y + 1 = 3 4(x + 3). y + 1 = 3 4 (x + 3). y 6 = 4 3 (x 8). y 6 = 4 3 (x 8) Which statement is always true?. cos J = RM RE. tan T = RM EM. cos R = JM JT. tan E = TM JM page 41

42 198. On the set of axes below, rectangle can be proven congruent to rectangle KLMN using which transformation? 199. In the diagram below, and F intersect at point, and and FE are drawn.. rotation. translation. reflection over the x-axis. reflection over the y-axis If = 6, = 4, F = 15, m = 65, and m E = 115, what is the length of? Seawater contains approximately 1.2 ounces of salt per liter on average. How many gallons of seawater, to the nearest tenth of a gallon, would contain 1 pound of salt? page 42

43 Problem-ttic format version c Educide Software Licensed for use by phelipedfernandes@gmail.com Terms of Use at 6/10/ G.O G.O.7 2. G.O G.O.8 3. G.O G.O.9 4. G.O G.O.9 5. G.O G.O.9 6. G.O [proof] G.O.9 7. G.O [proof] G.O G.O.2 G.O.2 G.O.2 G.O.3 G.O.6 G.O.6 G.O G.O.10 G.O.10 G.O.10 G.O.10 G.O.10 G.O.10

44 Teacher s Key Page G.O G.SRT G.O G.SRT Neither is correct G.O G.SRT = E; 5. Reflective property; 6. = E,SS; PT G.O = ; 2. defn. of angle bisector; 4. P = P, SS; 5. PT G.O.10 [proof] G.O.10 [proof] G.O.10 [proof] G.O.10 [proof] G.O.10 [proof] G.O.10 [proof] G.O.10 [proof] G.O.10 [proof] G.O.10 [proof] G.O.11 G.SRT G.SRT.5 G.SRT.6 G.SRT.6 G.SRT.6 G.SRT.7 G.SRT.8 G.SRT.8 G.SRT.11 [proof] G..1 [proof] G..1 G..1 G..2

45 Teacher s Key Page G G G G G G.GPE G.GPE (x 6) 2 + (y 4) 2 = 32 G.GPE G.GPE G.GPE G.GPE G.GPE G.GPE G.GM G.GM G.GM G.GM G.GM

46 Teacher s Key Page [proof] Since sine and cosine are cofunctions and and are complementary, sin = cos. Therefore when sin increases cos increases $1, No is dilated by a scale factor of 3 centered at point 108. v 586 m Mi; 6.2 Mi PT is isosceles because T = P; (2, 9); [proof]

47 Teacher s Key Page Yes Reflection over the origin and a translastion of (x 1, y + 1) [construction] = YZ 141. enter (3, 4) and radius [proof] [task] [task] ; 3752;

48 Teacher s Key Page π [construction] The volume of both triangular prisms are equal because avalieri s Principle states that if the base area and cross section of both prisms are the same, then the volumes are the same. 0.6 inches [explanation] 177. y = 3 4 x translation along vector F so maps onto F, followed by a rotation about F that maps to E and to F. [construction], [task], [explanation] [proof] 10.9 feet [proof]; [proof] 18,442 feet; 210 mph