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Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org49 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 6.947 In the diagram of circle A shown below, chords CDand EF intersect at G, and chords CE and FD aredrawn.G.GPE.1: EQUATIONS OF CIRCLES50 If x 2 4x y 2 6y 12 0 is the equation of acircle, the length of the radius is1 252 163 54 4Which statement is not always true?1 CG FG2 CEG FDGCEFD 3EG DGCEG FDG451 The equation of a circle is x 2 y 2 6y 7. Whatare the coordinates of the center and the length ofthe radius of the circle?1 center (0,3) and radius 42 center (0, 3) and radius 43 center (0,3) and radius 164 center (0, 3) and radius 16G.SRT.8, G.C.3: INSCRIBEDQUADRILATERALS48 In the diagram below, quadrilateral ABCD isinscribed in circle P.52 What are the coordinates of the center and lengthof the radius of the circle whose equation isx 2 6x y 2 4y 23 ?1 (3, 2) and 362 (3, 2) and 63 ( 3,2) and 364 ( 3,2) and 6What is m ADC ?1 70 2 72 3 108 4 110 12

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.orgG.GMD.4: CROSS-SECTIONS OFTHREE-DIMENSIONAL OBJECTSMEASURING IN THEPLANE AND SPACE55 Which figure can have the same cross section as asphere?G.GMD.4: ROTATIONS OFTWO-DIMENSIONAL OBJECTS53 Which object is formed when right triangle RSTshown below is rotated around leg RS ?121234a pyramid with a square basean isosceles trianglea right trianglea cone354 If the rectangle below is continuously rotated aboutside w, which solid figure is formed?12344pyramidrectangular prismconecylinder13

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org58 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 23056 William is drawing pictures of cross sections of theright circular cone below.59 As shown in the diagram below, a regular pyramidhas a square base whose side measures 6 inches.Which drawing can not be a cross section of acone?12If the altitude of the pyramid measures 12 inches,its volume, in cubic inches, is1 722 1443 2884 4323460 The diameter of a basketball is approximately 9.5inches and the diameter of a tennis ball isapproximately 2.5 inches. The volume of thebasketball is about how many times greater than thevolume of the tennis ball?1 35912 653 554 4G.GMD.3, G.MG.1: VOLUME57 A fish tank in the shape of a rectangular prism hasdimensions of 14 inches, 16 inches, and 10 inches.The tank contains 1680 cubic inches of water.What percent of the fish tank is empty?1 102 253 504 7514

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.orgG.MG.2: DENSITYG.GMD.1: CAVALERI’S PRINCIPLE61 Two stacks of 23 quarters each are shown below.One stack forms a cylinder but the other stack doesnot form a cylinder.63 During an experiment, the same type of bacteria isgrown in two petri dishes. Petri dish A has adiameter of 51 mm and has approximately 40,000bacteria after 1 hour. Petri dish B has a diameter of75 mm and has approximately 72,000 bacteria after1 hour.Use Cavelieri’s principle to explain why thevolumes of these two stacks of quarters are equal.G.MG.3: SURFACE AND LATERAL AREA62 A gallon of paint will cover approximately 450square feet. An artist wants to paint all the outsidesurfaces of a cube measuring 12 feet on each edge.What is the least number of gallons of paint hemust buy to paint the cube?1 12 23 34 4Determine and state which petri dish has thegreater population density of bacteria at the end ofthe first hour.64 A shipping container is in the shape of a rightrectangular prism with a length of 12 feet, a widthof 8.5 feet, and a height of 4 feet. The container iscompletely filled with contents that weigh, onaverage, 0.25 pound per cubic foot. What is theweight, in pounds, of the contents in the container?1 1,6322 4083 1024 9215

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org68 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?65 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.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?66 A contractor needs to purchase 500 bricks. Thedimensions of each brick are 5.1 cm by 10.2 cm by20.3 cm, and the density of each brick is1920 kg / m3 . The maximum capacity of thecontractor’s trailer is 900 kg. Can the trailer holdthe weight of 500 bricks? Justify your answer.69 Molly wishes to make a lawn ornament in the formof a solid sphere. The clay being used to make thesphere weighs .075 pound per cubic inch. If thesphere's radius is 4 inches, what is the weight of thesphere, to the nearest pound?1 342 203 154 467 Trees that are cut down and stripped of theirbranches for timber are approximately cylindrical.A timber company specializes in a certain type oftree that has a typical diameter of 50 cm and atypical height of about 10 meters. The density ofthe wood is 380 kilograms per cubic meter, and thewood can be sold by mass at a rate of 4.75 perkilogram. Determine and state the minimumnumber of whole trees that must be sold to raise atleast 50,000.70 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 261,38116

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.orgG.SRT.2, 5: TRIANGLE SIMILARITY71 The water tower in the picture below is modeled bythe two-dimensional figure beside it. The watertower is composed of a hemisphere, a cylinder, anda cone. Let C be the center of the hemisphere andlet D be the center of the base of the cone.72 The image of ABC after a dilation of scale factork centered at point A is ADE , as shown in thediagram below.Which statement is always true?1 2AB AD2 AD DE3 AC CE4 BC DEIf AC 8.5 feet, BF 25 feet, and m EFD 47 ,determine and state, to the nearest cubic foot, thevolume of the water tower. The water tower wasconstructed to hold a maximum of 400,000 poundsof water. If water weighs 62.4 pounds per cubicfoot, can the water tower be filled to 85% of itsvolume and not exceed the weight limit? Justifyyour answer.73 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 .Which relationship must always be true?m A 1 1m D 2m C 2 21m Fm A m F 3m C m Dm B m C 4m E m F17

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org74 In the diagram below, triangles XYZ and UVZ aredrawn such that X U and XZY UZV .76 Triangles ABC and DEF are drawn below.If AB 9, BC 15, DE 6, EF 10 , and B E , which statement is true?1 CAB DEFAB FE 2CB DE3ABC DEFAB FE 4DE CBDescribe a sequence of similarity transformationsthat shows XYZ is similar to UVZ .75 As shown in the diagram below, AB and CDintersect at E, and AC BD .77 In SCU shown below, points T and O are on SUand CU , respectively. Segment OT is drawn sothat C OTU .Given AEC CE EB 1DE EAAE AC 2BE BDEC BE 3AE EDED AC 4EC BDIf TU 4, OU 5, and OC 7, what is the lengthof ST ?1 5.62 8.753 114 15BED, which equation is true?18

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org78 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.81 In the diagram below,ABC DEF .If AB 6 and AC 8, which statement will justifysimilarity by SAS?1 DE 9, DF 12, and A D2 DE 8, DF 10, and A D3 DE 36, DF 64, and C F4 DE 15, DF 20, and C F79 The ratio of similarity of BOY to GRL is 1:2.If BO x 3 and GR 3x 1, then the length ofGR is1 52 73 104 2080 In the diagram below,ABC 82 In the diagram below,ABC ADE .DEC .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 15If AC 12, DC 7 , DE 5 , and the perimeter ofABC is 30, what is the perimeter of DEC ?1 12.52 14.03 14.84 17.519

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org83 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.86 In the diagram below, the line of sight from thepark ranger station, P, to the lifeguard chair, L, onthe beach of a lake is perpendicular to the pathjoining the campground, C, and the first aid station,F. The campground is 0.25 mile from the lifeguardchair. The straight paths from both thecampground and first aid station to the park rangerstation are perpendicular.Use the surveyor's information to determine andstate the distance from point B to point C, to thenearest yard.84 A flagpole casts a shadow 16.60 meters long. Timstands at a distance of 12.45 meters from the baseof the flagpole, such that the end of Tim's shadowmeets the end of the flagpole's shadow. If Tim is1.65 meters tall, determine and state the height ofthe flagpole to the nearest tenth of a meter.If the path from the park ranger station to thecampground is 0.55 mile, determine and state, tothe nearest hundredth of a mile, the distancebetween the park ranger station and the lifeguardchair. Gerald believes the distance from the firstaid station to the campground is at least 1.5 miles.Is Gerald correct? Justify your answer.G.SRT.5: RIGHT TRIANGLE SIMILARITY85 In the diagram below, CD is the altitude drawn tothe hypotenuse AB of right triangle ABC.Which lengths would not produce an altitude thatmeasures 6 2 ?1 AD 2 and DB 362 AD 3 and AB 243 AD 6 and DB 124 AD 8 and AB 1720

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org89 The line 3y 2x 8 is transformed by a dilationcentered at the origin. Which linear equation couldbe its image?1 2x 3y 52 2x 3y 53 3x 2y 54 3x 2y 5TRANSFORMATIONSG.SRT.1: LINE DILATIONS87 In the diagram below, CD is the image of AB aftera dilation of scale factor k with center E.90 The line y 2x 4 is dilated by a scale factor of32and centered at the origin. Which equationrepresents the image of the line after the dilation?1 y 2x 42 y 2x 63 y 3x 44 y 3x 691 The equation of line h is 2x y 1. Line m is theimage of line h after a dilation of scale factor 4with respect to the origin. What is the equation ofthe line m?1 y 2x 12 y 2x 43 y 2x 44 y 2x 1Which ratio is equal to the scale factor k of thedilation?EC1EABA2EAEA3BAEA4EC92 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 188 A line that passes through the points whosecoordinates are (1,1) and (5,7) is dilated by a scalefactor of 3 and centered at the origin. The image ofthe line1 is perpendicular to the original line2 is parallel to the original line3 passes through the origin4 is the original line93 Line is mapped onto line m by a dilation centeredat the origin with a scale factor of 2. The equationof line is 3x y 4. Determine and state anequation for line m.21

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.orgG.SRT.2: POLYGON DILATIONS96 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.94 If ABC is dilated by a scale factor of 3, whichstatement is true of the image A′B ′C ′?1 3A′B ′ AB2 B ′C ′ 3BC3 m A′ 3(m A)4 3(m C ′) m C95 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) .G.CO.5: IDENTIFYING TRANSFORMATIONS97 In the diagram below, which single transformationwas used to map triangle A onto triangle B?The ratio of the lengths of BE to CD is213322334443123422line reflectionrotationdilationtranslation

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org98 Triangle ABC and triangle DEF are graphed on theset of axes below.99 A sequence of transformations maps rectangleABCD onto rectangle A"B"C"D", as shown in thediagram below.Which sequence of transformations maps triangleABC onto triangle DEF?1 a reflection over the x-axis followed by areflection over the y-axis2 a 180 rotation about the origin followed by areflection over the line y x3 a 90 clockwise rotation about the originfollowed by a reflection over the y-axis4 a translation 8 units to the right and 1 unit upfollowed by a 90 counterclockwise rotationabout the originWhich 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 reflection23

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.orgG.CO.6: PROPERTIES OFTRANSFORMATIONS100 In the diagram below, congruent figures 1, 2, and 3are drawn.101 Quadrilateral ABCD is graphed on the set of axesbelow.When ABCD is rotated 90 in a counterclockwisedirection about the origin, its image is quadrilateralA'B'C'D'. Is distance preserved under this rotation,and which coordinates are correct for the givenvertex?1 no and C ' (1,2)2 no and D ' (2,4)3 yes and A ' (6,2)4 yes and B ' ( 3,4)Which sequence of transformations maps figure 1onto figure 2 and then figure 2 onto figure 3?1 a reflection followed by a translation2 a rotation followed by a translation3 a translation followed by a reflection4 a translation followed by a rotation102 Which transformation would result in the perimeterof a triangle being different from the perimeter ofits image?1 (x,y) (y,x)2 (x,y) (x, y)3 (x,y) (4x,4y)4 (x,y) (x 2,y 5)103 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 theorigin24

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org104 The vertices of JKL have coordinates J(5,1) ,K( 2, 3) , and L( 4,1). Under whichtransformation is the image J ′K ′L ′ notcongruent to JKL?1 a translation of two units to the right and twounits down2 a counterclockwise rotation of 180 degreesaround the origin3 a reflection over the x-axis4 a dilation with a scale factor of 2 and centeredat the origin106 Triangle ABC is graphed on the set of axes below.Graph and label A ' B ' C ', the image of ABCafter a reflection over the line x 1.105 The image of ABC after a rotation of 90ºclockwise about the origin is DEF , as shownbelow.107 Given right triangles ABC and DEF where C and F are right angles, AC DF and CB FE .Describe a precise sequence of rigid motions whichwould show ABC DEF .Which statement is true?1 BC DE2 AB DF3 C E4 A D25

Geometry Regents Exam Questions by Common Core State Standard: Topicwww.jmap.org108 In the diagram below,graphed.ABC and110 In the diagram below, AC DF and points A, C,D, and F are collinear on line .XYZ areLet D' E' F' be the image of DEF after atranslation along , such that point D

JMAP REGENTS BY COMMON CORE STATE STANDARD: TOPIC NY Geometry Regents Exam Questions from Spri