# 0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn.

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1 0615geo 1 Which object is formed when right triangle RST shown below is rotated around leg RS? 4 In the diagram below, congruent figures 1, 2, and 3 are drawn. 1) a pyramid with a square base 2) an isosceles triangle 3) a right triangle 4) a cone 2 The vertices of JKL have coordinates J(5,1), K( 2, 3), and L( 4,1). Under which transformation is the image J K L not congruent to JKL? 1) a translation of two units to the right and two units down 2) a counterclockwise rotation of 180 degrees around the origin 3) a reflection over the x-axis 4) a dilation with a scale factor of 2 and centered at the origin 3 The center of circle Q has coordinates (3, 2). If circle Q passes through R(7,1), what is the length of its diameter? 1) 50 2) 25 3) 10 4) 5 Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3? 1) a reflection followed by a translation 2) a rotation followed by a translation 3) a translation followed by a reflection 4) a translation followed by a rotation 5 As shown in the diagram below, the angle of elevation from a point on the ground to the top of the tree is 34. If the point is 20 feet from the base of the tree, what is the height of the tree, to the nearest tenth of a foot? 1) ) ) )

2 6 Which figure can have the same cross section as a sphere? 8 In the diagram of circle A shown below, chords CD and EF intersect at G, and chords CE and FD are drawn. 1) 2) 3) 4) 7 A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet, and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pound per cubic foot. What is the weight, in pounds, of the contents in the container? 1) 1,632 2) 408 3) 102 4) 92 Which statement is not always true? 1) CG FG 2) CEG FDG 3) CE EG = FD DG 4) CEG FDG 9 Which equation represents a line that is perpendicular to the line represented by 2x y = 7? 1) y = 1 2 x + 6 2) y = 1 2 x + 6 3) y = 2x + 6 4) y = 2x Which regular polygon has a minimum rotation of 45 to carry the polygon onto itself? 1) octagon 2) decagon 3) hexagon 4) pentagon 2

3 11 In the diagram of ADC below, EB DC, AE = 9, ED = 5, and AB = The equation of a circle is x 2 + y 2 + 6y = 7. What are the coordinates of the center and the length of the radius of the circle? 1) center (0,3) and radius 4 2) center (0, 3) and radius 4 3) center (0,3) and radius 16 4) center (0, 3) and radius Triangles ABC and DEF are drawn below. What is the length of AC, to the nearest tenth? 1) 5.1 2) 5.2 3) ) In scalene triangle ABC shown in the diagram below, m C = 90. Which equation is always true? 1) sina = sinb 2) cos A = cos B 3) cos A = sinc 4) sina = cos B 13 Quadrilateral ABCD has diagonals AC and BD. Which information is not sufficient to prove ABCD is a parallelogram? 1) AC and BD bisect each other. 2) AB CD and BC AD 3) AB CD and AB CD 4) AB CD and BC AD If AB = 9, BC = 15, DE =6, EF = 10, and B E, which statement is true? 1) CAB DEF 2) AB CB = FE DE 3) ABC DEF 4) AB DE = FE CB 16 If ABC is dilated by a scale factor of 3, which statement is true of the image A B C? 1) 3A B = AB 2) B C = 3BC 3) m A = 3(m A) 4) 3(m C ) = m C 3

4 17 Steve drew line segments ABCD, EFG, BF, and CF as shown in the diagram below. Scalene BFC is formed. Which statement will allow Steve to prove ABCD EFG? 1) CFG FCB 2) ABF BFC 3) EFB CFB 4) CBF GFC 19 A gallon of paint will cover approximately 450 square feet. An artist wants to paint all the outside surfaces of a cube measuring 12 feet on each edge. What is the least number of gallons of paint he must buy to paint the cube? 1) 1 2) 2 3) 3 4) 4 20 In circle O shown below, diameter AC is perpendicular to CD at point C, and chords AB, BC, AE, and CE are drawn. 18 In the diagram below, CD is the image of AB after a dilation of scale factor k with center E. Which statement is not always true? 1) ACB BCD 2) ABC ACD 3) BAC DCB 4) CBA AEC 21 In the diagram below, ABC DEC. Which ratio is equal to the scale factor k of the dilation? 1) EC EA 2) BA EA 3) EA BA 4) EA EC If AC = 12, DC = 7, DE = 5, and the perimeter of ABC is 30, what is the perimeter of DEC? 1) ) ) )

5 22 The line 3y = 2x + 8 is transformed by a dilation centered at the origin. Which linear equation could be its image? 1) 2x + 3y = 5 2) 2x 3y = 5 3) 3x + 2y = 5 4) 3x 2y = 5 25 Use a compass and straightedge to construct an inscribed square in circle T shown below. [Leave all construction marks.] 23 A circle with a radius of 5 was divided into 24 congruent sectors. The sectors were then rearranged, as shown in the diagram below. To the nearest integer, the value of x is 1) 31 2) 16 3) 12 4) The diagram below shows parallelogram LMNO with diagonal LN, m M = 118, and m LNO = Which statement is sufficient evidence that DEF is congruent to ABC? Explain why m NLO is 40 degrees. 1) AB = DE and BC = EF 2) D A, B E, C F 3) There is a sequence of rigid motions that maps AB onto DE, BC onto EF, and AC onto DF. 4) There is a sequence of rigid motions that maps point A onto point D, AB onto DE, and B onto E. 5

6 27 The coordinates of the endpoints of AB are A( 6, 5) and B(4,0). Point P is on AB. Determine and state the coordinates of point P, such that AP:PB is 2:3. [The use of the set of axes below is optional.] 29 In the diagram below of circle O, the area of the shaded sector AOC is 12π in 2 and the length of OA is 6 inches. Determine and state m AOC. 30 After a reflection over a line, A B C is the image of ABC. Explain why triangle ABC is congruent to triangle A B C. 28 The diagram below shows a ramp connecting the ground to a loading platform 4.5 feet above the ground. The ramp measures feet from the ground to the top of the loading platform. 31 A flagpole casts a shadow meters long. Tim stands at a distance of meters from the base of the flagpole, such that the end of Tim's shadow meets the end of the flagpole's shadow. If Tim is 1.65 meters tall, determine and state the height of the flagpole to the nearest tenth of a meter. Determine and state, to the nearest degree, the angle of elevation formed by the ramp and the ground. 6

7 32 In the diagram below, EF intersects AB and CD at G and H, respectively, and GI is drawn such that GH IH. 34 In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F. The campground is 0.25 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular. If m EGB = 50 and m DIG = 115, explain why AB CD. 33 Given: Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E If the path from the park ranger station to the campground is 0.55 mile, determine and state, to the nearest hundredth of a mile, the distance between the park ranger station and the lifeguard chair. Gerald believes the distance from the first aid station to the campground is at least 1.5 miles. Is Gerald correct? Justify your answer. Prove: AED CEB Describe a single rigid motion that maps onto CEB. AED 7

8 35 The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower is composed of a hemisphere, a cylinder, and a cone. Let C be the center of the hemisphere and let D be the center of the base of the cone. 36 In the coordinate plane, the vertices of RST are R(6, 1), S(1, 4), and T( 5,6). Prove that RST is a right triangle. State the coordinates of point P such that quadrilateral RSTP is a rectangle. Prove that your quadrilateral RSTP is a rectangle. [The use of the set of axes below is optional.] If AC = 8.5 feet, BF = 25 feet, and m EFD = 47, determine and state, to the nearest cubic foot, the volume of the water tower. The water tower was constructed to hold a maximum of 400,000 pounds of water. If water weighs 62.4 pounds per cubic foot, can the water tower be filled to 85% of its volume and not exceed the weight limit? Justify your answer. 8

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