GEOMETRY (Common Core)

1 The University of the State of New YorkREGENTS HIGH SCHOOL EXAMINATIONGEOMETRY (Common Core) Tuesday,June 2, 2015 1:15 to 4:15 , onlyStudent Name:_____School Name:_____Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow theinstructions from the proctor for completing the student information on your examination has four parts, with a total of 36 questions. You must answerall questions in this examination. Record your answers to the Part I multiple-choicequestions on the separate answer sheet. Write your answers to the questions inParts II, III, and IV directly in this booklet. All work should be written in pen,except for graphs and drawings, which should be done in pencil. Clearly indicatethe necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine youranswer.

2 Note that diagrams are not necessarily drawn to formulas that you may need to answer some questions in this examinationare found at the end of the examination. This sheet is perforated so you mayremove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may usethe blank spaces in this booklet as scrap paper. A perforated sheet of scrap graphpaper is provided at the end of this booklet for any question for which graphingmay be helpful but is not required. You may remove this sheet from this work done on this sheet of scrap graph paper will notbe you have completed the examination, you must sign the statement printedat the end of the answer sheet, indicating that you had no unlawful knowledge ofthe questions or answers prior to the examination and that you have neither givennor received assistance in answering any of the questions during the answer sheet cannot be accepted if you fail to sign this (COMMON Core) DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS graphing calculator, a straightedge (ruler), and a compass must be available for you to use while taking this (COMMON Core) The possession or use of any communications device is strictly prohibited when taking this examination.

3 If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for object is formed when right triangle RSTshown below isrotated around leg RS___?(1) a pyramid with a square base (3) a right triangle(2) an isosceles triangle(4) a cone2 The vertices of JKLhave coordinates J(5,1), K( 2, 3), andL( 4,1). Under which transformation is the image J K L notcongruent 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 origin3 The center of circle Qhas coordinates (3, 2). If circle Qpassesthrough R(7,1), what is the length of its diameter?(1) 50(3) 10(2) 25(4) 5 RTSUse this space IAnswer all 24 questions in this part. Each correct answer will receive 2 credits.

4 Utilize theinformation provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that,of those given, best completes the statement or answers the question.[48] GEOMETRY (Common Core) June 15[2]Use this space the diagram below, congruent figures 1, 2, and 3 are sequence of transformations maps figure 1 onto figure 2 andthen 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 rotation5As shown in the diagram below, the angle of elevation from a pointon 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 heightof the tree, to the nearest tenth of a foot?(1) (3) (2) (4) E C C D E 123 FBAA B F F B A GEOMETRY (Common Core) June 15[3][OVER] GEOMETRY (Common Core) June 15[4]6 Which figure can have the same cross section as a sphere?

5 7A shipping container is in the shape of a right rectangular prism witha length of 12 feet, a width of feet, and a height of 4 feet. Thecontainer is completely filled with contents that weigh, on average, pound per cubic foot. What is the weight, in pounds, of the contents in the container?(1) 1,632(3) 102(2) 408(4) 92(1)(3)(2)(4)Use this space (Common Core) June 15[5][OVER]8In the diagram of circle Ashown below, chords CD___and EF___intersectat G, and chords CE___and FD___ are statement is notalways true?(1)CG___ FG___(3)(2) CEG FDG(4) CEG~ FDG9 Which equation represents a line that is perpendicular to the linerepresented by 2x y 7?(1)y 1__2 x 6(3)y 2x 6(2)y 1__2 x 6(4)y 2x 6 CEEG FDDGCFDGAEUse this space this space regular polygon has a minimum rotation of 45 to carry thepolygon onto itself?(1) octagon(3) hexagon(2) decagon(4) pentagon11In the diagram of ADCbelow, EB___||DC___, AE 9, ED 5, andAB is the length ofAC___, to the nearest tenth?

6 (1) (3) (2) (4) (Common Core) June 15[6]Use this space scalene triangle ABCshown in the diagram below, m C 90 .Which equation is always true?(1) sin A sin B(3) cos A sin C(2) cos A cos B(4) sin A cos B13 Quadrilateral ABCDhas diagonals AC___and BD___. Which informationis notsufficient to prove ABCDis 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___14 The equation of a circle is x2 y2 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 16 ACBG eometry (Common Core) June 15[7][OVER]Use this space ABCand DEFare drawn AB 9, BC 15, DE 6, EF 10, and B E, which statement is true?(1) CAB DEF(3) ABC~ DEF(2)(4)16If ABC is dilated by a scale factor of 3, which statement is true ofthe image A B C ?

7 (1) 3A B AB(3) m A 3(m A)(2)B C 3BC(4) 3(m C ) m CABDEFECB ABCBFEDE ABCEDFG eometry (Common Core) June 15[8]Use this space drew line segments ABCD, EFG, BF, and CFas shown in thediagram below. Scalene BFCis statement will allow Steve to prove ||?(1) CFG FCB(3) EFB CFB(2) ABF BFC(4) CBF GFC18In the diagram below, CD___is the image of AB___after a dilation of scalefactor kwith center ratio is equal to the scale factor kof the dilation?(1)(3)(2)(4)ECEABAEAEAECEABAyxA BDECABCDEFGEFGABCDG eometry (Common Core) June 15[9][OVER]Use this space gallon of paint will cover approximately 450 square feet. An artistwants to paint all the outside surfaces of a cube measuring 12 feeton each edge. What is the leastnumber of gallons of paint he mustbuy to paint the cube?(1) 1(3) 3(2) 2(4) 420In circle Oshown below, diameter AC___is perpendicular toCD___atpoint C, and chords AB___,BC___, AE___, and CE___are statement is notalways true?

8 (1) ACB BCD(3) BAC DCB(2) ABC ACD(4) CBA AEC21In the diagram below, ABC ~ AC 12, DC 7, DE 5, and the perimeter of ABCis 30,what is the perimeter of DEC?(1) (3) (2) (4) (Common Core) June 15[10]Use this space line 3y 2x 8 is transformed by a dilation centered at theorigin. Which linear equation could be its image?(1) 2x 3y 5(3)3x 2y 5(2) 2x 3y 5(4)3x 2y 523A circle with a radius of 5 was divided into 24 congruent sectors. Thesectors were then rearranged, as shown in the diagram the nearest integer, the value of xis (1) 31(3) 12(2) 16(4) 1024 Which statement is sufficient evidence that DEFis congruent to ABC?(1)AB DEand 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 Aontopoint D,AB___onto DE___,and B onto (Common Core) June 15[11][OVER]Part IIAnswer all 7 questions in this part.

9 Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.[14]25 Use a compass and straightedge to construct an inscribed square in circle Tshown below. [Leave all construction marks.]TGeometry (Common Core) June 15[12]26 The diagram below shows parallelogram LMNO with diagonal LN___, m M 118 , andm LNO 22 .Explain why m NLOis 40 (Common Core) June 15[13][OVER]27 The coordinates of the endpoints of AB___are A( 6, 5) and B(4,0).

10 Point Pis on AB___. Determineand state the coordinates of point P, such that AP:PBis 2:3.[The use of the set of axes below is optional.]yxGeometry (Common Core) June 15[14]28 The diagram below shows a ramp connecting the ground to a loading platform feet above theground. The ramp measures feet from the ground to the top of the loading and state, to the nearest degree, the angle of elevation formed by the ramp and ftGeometry (Common Core) June 15[15][OVER]29In the diagram below of circle O, the area of the shaded sector AOCis 12 in2and the length ofOA___is 6 inches. Determine and state m AOC. GEOMETRY (Common Core) June 15[16]30 After a reflection over a line, A B C is the image of ABC. Explain why triangle ABCis congruent to triangle A B C . GEOMETRY (Common Core) June 15[17][OVER]31A flagpole casts a shadow meters long. Tim stands at a distance of meters from thebase of the flagpole, such that the end of Tim s shadow meets the end of the flagpole s Tim is meters tall, determine and state the height of the flagpole to the nearest tenth of (Common Core) June 15[18]32In the diagram below,EF___intersects AB___and CD___at Gand H, respectively, and GI___is drawn suchthat GH___ m EGB 50 and m DIG 115 , explain why AB___||CD___.