0815geo - Mr. Beach's Site

Geometry CCSS Regents Exam 0815www.jmap.org0815geo1 A parallelogram must be a rectangle when its1) diagonals are perpendicular2) diagonals are congruent3) opposite sides are parallel4) opposite sides are congruent5 In the diagram below, a square is graphed in thecoordinate plane.2 If A' B' C' is the image of ABC , under whichtransformation will the triangles not be congruent?1) reflection over the x-axis2) translation to the left 5 and down 43) dilation centered at the origin with scale factor24) rotation of 270 counterclockwise about theoriginA reflection over which line does not carry thesquare onto itself?1) x 52) y 23) y x4) x y 43 If the rectangle below is continuously rotated aboutside w, which solid figure is formed?1)2)3)4)6 The image of ABC after a dilation of scale factork centered at point A is ADE , as shown in thediagram below.pyramidrectangular prismconecylinder4 Which expression is always equivalent to sinxwhen 0 x 90 ?1) cos(90 x)2) cos(45 x)3) cos(2x)4) cos xWhich statement is always true?1) 2AB AD2) AD DE3) AC CE4) BC DE1

Geometry CCSS Regents Exam 0815www.jmap.org7 A sequence of transformations maps rectangleABCD onto rectangle A"B"C"D", as shown in thediagram below.9 If x 2 4x y 2 6y 12 0 is the equation of acircle, the length of the radius is1) 252) 163) 54) 410 Given MN shown below, with M( 6,1) andN(3, 5), what is an equation of the line that passesthrough point P(6,1) and is parallel to MN ?Which sequence of transformations maps ABCDonto A'B'C'D' and then maps A'B'C'D' ontoA"B"C"D"?1) a reflection followed by a rotation2) a reflection followed by a translation3) a translation followed by a rotation4) a translation followed by a reflection8 In the diagram of parallelogram FRED shownbelow, ED is extended to A, and AF is drawn suchthat AF DF .1)2)3)4)If m R 124 , what is m AFD ?1) 124 2) 112 3) 68 4) 56 22y x 532y x 333y x 723y x 82

Geometry CCSS Regents Exam 0815www.jmap.org11 Linda is designing a circular piece of stained glasswith a diameter of 7 inches. She is going to sketcha square inside the circular region. To the nearesttenth of an inch, the largest possible length of aside of the square is1) 3.52) 4.93) 5.04) 6.913 In the diagram below, which single transformationwas used to map triangle A onto triangle B?12 In the diagram shown below, AC is tangent tocircle O at A and to circle P at C, OP intersects ACat B, OA 4, AB 5, and PC 10 .1)2)3)4)line reflectionrotationdilationtranslation14 In the diagram below, DEF is the image ofABC after a clockwise rotation of 180 and adilation where AB 3, BC 5.5, AC 4.5,DE 6 , FD 9 , and EF 11 .What is the length of BC ?1) 6.42) 83) 12.54) 16Which relationship must always be true?m A 1 1)m D 2m C 2 2)1m Fm A m F 3)m C m Dm B m C 4)m E m F3

Geometry CCSS Regents Exam 0815www.jmap.org17 In the diagram below,15 In the diagram below, quadrilateral ABCD isinscribed in circle P.ABC ADE .Which measurements are justified by thissimilarity?1) AD 3, AB 6, AE 4, and AC 122) AD 5, AB 8, AE 7, and AC 103) AD 3, AB 9, AE 5, and AC 104) AD 2, AB 6, AE 5, and AC 15What is m ADC ?1) 70 2) 72 3) 108 4) 110 18 Triangle FGH is inscribed in circle O, the length ofradius OH is 6, and FH OG.16 A hemispherical tank is filled with water and has adiameter of 10 feet. If water weighs 62.4 poundsper cubic foot, what is the total weight of the waterin a full tank, to the nearest pound?1) 16,3362) 32,6733) 130,6904) 261,381What is the area of the sector formed by angleFOH?1) 2π3π2)23) 6π4) 24π4

Geometry CCSS Regents Exam 0815www.jmap.org21 The Great Pyramid of Giza was constructed as aregular pyramid with a square base. It was builtwith an approximate volume of 2,592,276 cubicmeters and a height of 146.5 meters. What was thelength of one side of its base, to the nearest meter?1) 732) 773) 1334) 23019 As shown in the diagram below, AB and CDintersect at E, and AC BD .Given AEC CE EB 1)DE EAAE AC 2)BE BDEC BE 3)AE EDED AC 4)EC BD22 A quadrilateral has vertices with coordinates( 3,1), (0,3), (5,2), and ( 1, 2). Which type ofquadrilateral is this?1) rhombus2) rectangle3) square4) trapezoidBED, which equation is true?20 A triangle is dilated by a scale factor of 3 with thecenter of dilation at the origin. Which statement istrue?1) The area of the image is nine times the· area ofthe original triangle.2) The perimeter of the image is nine times theperimeter of the original triangle.3) The slope of any side of the image is threetimes the slope of the corresponding side of theoriginal triangle.4) The measure of each angle in the image is threetimes the measure of the corresponding angleof the original triangle.5

Geometry CCSS Regents Exam 0815www.jmap.org23 In the diagram below, ABE is the image ofACD after a dilation centered at the origin. Thecoordinates of the vertices are A(0,0), B(3,0) ,C(4.5,0), D(0,6) , and E(0,4) .25 A wooden cube has an edge length of 6 centimetersand a mass of 137.8 grams. Determine the densityof the cube, to the nearest thousandth. State whichtype of wood the cube is made of, using the densitytable below.The ratio of the lengths of BE to CD is21)332)233)444)326 Construct an equilateral triangle inscribed in circleT shown below. [Leave all construction marks.]24 Line y 3x 1 is transformed by a dilation with ascale factor of 2 and centered at (3,8). The line'simage is1) y 3x 82) y 3x 43) y 3x 24) y 3x 16

Geometry CCSS Regents Exam 0815www.jmap.org27 To find the distance across a pond from point B topoint C, a surveyor drew the diagram below. Themeasurements he made are indicated on hisdiagram.30 In the diagram below,graphed.ABC andXYZ areUse the surveyor's information to determine andstate the distance from point B to point C, to thenearest yard.Use the properties of rigid motions to explain whyABC XYZ .28 In parallelogram ABCD shown below, diagonalsAC and BD intersect at E.31 The endpoints of DEF are D(1,4) and F(16,14) .Determine and state the coordinates of point E, ifDE:EF 2:3.Prove: ACD CAB32 As shown in the diagram below, a ship is headingdirectly toward a lighthouse whose beacon is 125feet above sea level. At the first sighting, point A,the angle of elevation from the ship to the light was7 . A short time later, at point D, the angle ofelevation was 16 .29 Triangles RST and XYZ are drawn below. IfRS 6 , ST 14, XY 9, YZ 21, and S Y , isRST similar to XYZ ? Justify your answer.To the nearest foot, determine and state how far theship traveled from point A to point D.7

Geometry CCSS Regents Exam 0815www.jmap.org33 Triangle ABC has vertices with A(x,3), B( 3, 1) ,and C( 1, 4). Determine and state a value of xthat would make triangle ABC a right triangle.Justify why ABC is a right triangle. [The use ofthe set of axes below is optional.]35 In the diagram of parallelogram ABCD below,BE CED, DF BFC , CE CF .Prove ABCD is a rhombus.36 Walter wants to make 100 candles in the shape of acone for his new candle business. The mold shownbelow will be used to make the candles. Each moldwill have a height of 8 inches and a diameter of 3inches. To the nearest cubic inch, what will be thetotal volume of 100 candles?34 In the diagram below, AC DF and points A, C,D, and F are collinear on line .Walter goes to a hobby store to buy the wax for hiscandles. The wax costs 0.10 per ounce. If theweight of the wax is 0.52 ounce per cubic inch,how much will it cost Walter to buy the wax for100 candles? If Walter spent a total of 37.83 forthe molds and charges 1.95 for each candle, whatis Walter's profit after selling 100 candles?Let D' E' F' be the image of DEF after atranslation along , such that point D is mappedonto point A. Determine and state the location ofF'. Explain your answer. Let D"E"F" be theimage of D' E' F' after a reflection across line .Suppose that E" is located at B. Is DEFcongruent to ABC ? Explain your answer.8

36 Walter wants to make 100 candles in the shape of a cone for his new candle business. The mold shown below will be used to make the candles. Each mold will have a height of 8 inches and a diameter of 3 inches. To the nearest cubic inch, what will be the total volume of 100 candles? Walter goes to a hobby store to buy the wax for his candles.