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GeometryAdministered May 2013RELEASEDCopyright 2013, Texas Education Agency. All rights reserved. Reproduction of all or portions of this work is prohibited without expresswritten permission from the Texas Education Agency.TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 16/25/13 3:00 PM

TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 25/28/2013 3:21:44 PMSTAAR

STAARSTAAR GEOMETRYREFERENCE MATERIALSTMState of TexasAssessments ofAcademic ReadinessCIRCUMFERENCECircleC 2π rorC πdAREATriangleA 1 bh2Rectangle or parallelogramA bhRhombusA 1 d1d22TrapezoidA 1 (b1 b2)h2Regular polygonA CircleA πr21aP2SURFACE AREALateralTotalPrismS PhS Ph 2BPyramidS 1 Pl2S 1 Pl B2CylinderS 2π rhS 2π rh 2πr 2ConeS πr lS πr l πr 2SphereS 4π r 2VOLUMEPrism or cylinderV BhPyramid or coneV 1 Bh3SphereV 4 πr 33Page 3TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd3STAAR Geometry Reference Materials.indd 15/28/20133:21:44 PMPM12/9/11 2:31:50

STAAR GEOMETRYREFERENCE MATERIALSCOORDINATE GEOMETRYMidpoint(Distance formulad Slope of a linem Slope-intercept form of a linear equationy mx bPoint-slope form of a linear equationy y1 m(x x1)Standard form of a linear equationAx By Cx1 x2 y1 y2,22)(x2 x1)2 (y2 y1)2y2 y1x2 x1RIGHT TRIANGLESa2 b2 c 2Pythagorean theoremTrigonometric ratiosBopposite legsin A hypotenusecos A adjacent leghypotenusetan A opposite legadjacent legA30 – 60 – 90 triangleC45 – 45 – 90 triangle60 2xx45 30 x 345 x 2xxPage 4TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd4STAAR Geometry Reference Materials.indd 25/28/20133:21:44 PMPM12/9/11 2:31:52

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DIRECTIONSRead each question carefully. For a multiple-choice question, determine the bestanswer to the question from the four answer choices provided. For a griddable question,determine the best answer to the question. Then fill in the answer on your answerdocument.1CD has an endpoint at (2, 1) and a midpoint at (8, 3). Which measure is closest to thelength of CD ?A20.4 unitsB8.9 unitsC14.4 unitsD 11.7 units2Isosceles trapezoid JKLM is shown below.39 unitsJK120 17 unitsM56 unitsLIf the dimensions of trapezoid JKLM are multiplied by a scale factor of f to create trapezoidJ ′K ′L′M ′, which statement is true?FTrapezoid J ′K ′L′M ′ contains two base angles measuring 30 each.G The longer base of trapezoid J ′K ′L′M ′ is 56f units.H The bases of trapezoid J ′K ′L′M ′ have lengths of 22 units and 39 units.JTrapezoid J ′K ′L′M ′ contains two base angles measuring (120f ) each.Page 9TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 95/28/2013 3:21:44 PM

3Which pair of triangles has enough given information to prove that the triangles arecongruent?ABCD None of these4In the diagram below, the angle of depression from P to Q is 45 .P45 Cliff32 ftQNot drawn to scaleWhich of the following is closest to the distance between P and Q?F45.3 ftG 22.6 ftH 55.4 ftJ18.5 ftPage 10TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 105/28/2013 3:21:44 PM

5The rectangular pyramid shown below was intersected by a plane parallel to base ABCD toform quadrilateral A′B′C ′D ′ .FA’D’DAB’C’BCBased on this information, which statement cannot be proved true?6AABCD A′B′C ′D ′CBAFBF A′FB′FD BCD B′C′D′ AA ′D ′ BB′A′Five spheres are being painted for a display at a store. If the diameter of each sphere is7 centimeters, which value is closest to the total surface area that will be painted?F770 cm2G154 cm2H192 cm2J440 cm2Page 11TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 115/28/2013 3:21:45 PM

7On the map below, Main Street, 10th Street, and Highway 1 intersect to form a right triangle.MHighway 1ainSt.40 10th St.The distance between 10th Street and Main Street along Highway 1 is 5.6 mi. Which measureis closest to the length of Main Street from Highway 1 to 10th Street?8A8.7 miC4.7 miB3.6 miD 7.3 miFor triangles ABC and DEF, A D and B E. Based on this information, whichstatement is a reasonable conclusion?F C D because they are corresponding angles of congruent triangles.GCA FD because they are corresponding parts of congruent triangles.H C F because they are corresponding angles of similar triangles.JAB DE because they are corresponding parts of similar triangles.Page 12TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 125/28/2013 3:21:45 PM

9andare secants of circle V, as shown below.XW60 U72 VYZBased on this information, which of the following can be proved true?Am ZUY m ZVYBm XUY 12(mWZ mXY)CmWX 180 mWZDm WUX 12(mZY mWX)Page 13TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 135/28/2013 3:21:45 PM

10PQ is shown on the coordinate grid below. The coordinates of P and Q are 2–3–4–5Point (x, y) lies on the perpendicular bisector of PQ. What is the value of x?Record your answer and fill in the bubbles on your answer document.11 A conditional statement is given below.If two interior angles of a triangle are acute,then the third interior angle must be obtuse.Which of the following best describes this statement?AThis statement is true because all obtuse triangles have two acute interior angles.BThis statement is false because the third interior angle must also be acute.CThis statement is true because a triangle can have at most one interior obtuse angle.D This statement is false because the third interior angle can be acute, right, or obtuse.Page 14TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 145/28/2013 3:21:45 PM

12 The side length of a smaller square is one-third the side length of a larger square. Which ofthe following statements describes the area of the smaller square?FThe area of the smaller square isG The area of the smaller square isH The area of the smaller square isJThe area of the smaller square is127161913the area of the larger square.the area of the larger square.the area of the larger square.the area of the larger square.13 A pattern of dots is shown in the four figures below.Figure 1Figure 2Figure 3Figure 4If the pattern continues, which expression can be used to find the total number of dots inFigure n?A3n 5B2n 2C2n 3D3n 1Page 15TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 155/28/2013 3:21:45 PM

14 The equation of a line containing one leg of a right triangle is y 4x. Which of thefollowing equations could represent the line containing the other leg of this triangle?Fy Gy 141xHy 4xx 2Jy 4x 2415 Two regular hexagons with center C and apothems a and b are shown in the figure below.Each vertex of the smaller hexagon is a midpoint on a side of the larger hexagon.bCaIf a 12 3 cm and b 18 cm, what is the total area of the shaded regions?A648 3 cm2B36 3 cm2C216 3 cm2D1,512 3 cm2Page 16TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 165/28/2013 3:21:45 PM

16 The two conditional statements below are true.If 3 and 4 form a linear pair, then they are supplementary.If 3 and 4 are supplementary, then m 3 m 4 180 .Based on these conditional statements, which statement must also be true?FIf 3 and 4 form a linear pair, then m 3 m 4 180 .G If 3 and 4 form a linear pair, then m 3 90 , and m 4 90 .H If m 3 m 4 180 , then 3 and 4 form a linear pair.JIf 3 and 4 are supplementary, then 3 and 4 form a linear pair.17 Rectangle STUW is shown below.ST20 in.W8 in.VU5 in.What is ST ?A33 in.B24 in.C464 in.D361 in.Page 17TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 175/28/2013 3:21:45 PM

18 A statement is given below.The number of square units in the area of a square is greater than or equal to the numberof units in the perimeter of the square.Which side length of a square provides a counterexample to the given statement?F6 unitsG 4 unitsH 10 unitsJ2 units19 The table below contains a pattern formed by the number of sides and the measure indegrees of each exterior angle of several regular convex polygons.Exterior Angle Measures of Regular PolygonsNumber of Sides3Exterior Angle120Measure (degrees)456101520459090726036241884If the pattern in the table continues, which statement is true?AAs the number of sides in the polygon increases by 1, the measure of each exteriorangle decreases by 25%.BThe product of the number of sides in the polygon and the measure of each exteriorangle is a constant.CThe measure of each exterior angle is a multiple of 6 degrees.D If the number of sides in the polygon is even, the measure of each exterior angle is amultiple of 3 degrees.Page 18TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 185/28/2013 3:21:45 PM

20 The volume of a rectangular prism is 960 cubic inches. If the dimensions of the base aredoubled and the height remains the same to create a new prism, what will be the volume ofthe new rectangular prism in cubic inches?Record your answer and fill in the bubbles on your answer document.21 The hand on the circular clock in the figure below measures 10 cm.11 12 11023987 654Which of the following is closest to the distance that the tip of the hand travels as it movesfrom the 12 to the 3?A79 cmB21 cmC63 cmD 16 cm22 A plane intersects a cylinder. Which of the following cannot be formed by this intersection?FTriangleG LineH RectangleJCirclePage 19TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 195/28/2013 3:21:45 PM

23 Which expression can be used to find the length of QR in centimeters?Q20 RA19(cos 20 )B19(tan 20 )C19(sin 70 )S19 cmD 19(tan 70 )24 In circle E below, AEB CED.ABECDBased on this information, which statement must be true?FAB CDGEB ECHm AED 4(m DEC)Jm AEB m DEC m BECPage 20TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 205/28/2013 3:21:45 PM

25 The graph of line g is shown below.y109876(–4, 6)54(4, 2)321 10 9 8 7 6 5 4 3 2 1 1123456789 10xg 2 3 4 5 6 7 8 9 10Which equation describes a line parallel to line g that has a y-intercept at (0, 1)?Ay 2x 1By 12x 11Cy Dy 2x 12x 1Page 21TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 215/28/2013 3:21:46 PM

26 Three gears in a machine are positioned relative to each other to form an isosceles righttriangle, as shown below.A9.1B2 cmCWhat is the distance in centimeters between the centers of the gears located at B and C ?Record your answer and fill in the bubbles on your answer document.27 The following conditional statement is true.If a quadrilateral is a square, then it has four congruent sides.Which statement must also be true?AIf a quadrilateral has four congruent sides, then it is a square.BIf a quadrilateral does not have four congruent sides, then it is not a square.CIf a quadrilateral is not a square, then it does not have four congruent sides.D If a quadrilateral does not have four congruent sides, then it is a square.Page 22TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 225/28/2013 3:21:46 PM

28 A conical paper cup is shown in the diagram below.4.5 cm6 cm7.5 cmWhich value is closest to the maximum volume of water this cup can hold?F159 cm3G32 cm3H127 cm3J40 cm3329 The slope of a line passing through H( 2, 5) is . Which ordered pair represents a point on4this line?A(6, 1)B(2, 8)C( 5, 1)D(1, 1)Page 23TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 235/28/2013 3:21:46 PM

30 Which statement about a triangular prism is true?FA triangular prism has 4 faces, 6 edges, and 4 vertices.G A triangular prism has 3 faces, 6 edges, and 3 vertices.H A triangular prism has 5 faces, 9 edges, and 6 vertices.JA triangular prism has 6 faces, 11 edges, and 8 vertices.Page 24TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 245/28/2013 3:21:46 PM

31 InQRS, RTis an altitude.R5 cmQTS3 cmWhich additional condition would not be sufficient to prove that QR SR?AT is the midpoint of QS.B RT bisects QRS.C TS 2 cmD RT 4 cmPage 25TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 255/28/2013 3:21:46 PM

32 Lines r, t, n, and v intersect as shown to form isosceles trapezoid ABCD.rt1BnCAD(7y 4) vWhich expression represents the measure of 1 in degrees?F180 (7y 4)H(7y 4)G180 2(7y 4)J180 (7y 4)33 A banner is composed of two congruent triangles and a rectangle, as shown below.12 cm10 cm17 cmWhat is the total area of the banner in square centimeters?Record your answer and fill in the bubbles on your answer document.Page 26TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 265/28/2013 3:21:46 PM

34 The front, side, and top views of a three-dimensional figure made of identical cubes areshown below.Top viewFront viewSide viewWhich diagram best represents this three-dimensional figure?FHntntFroGFroJntFrontFroPage 27TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 275/28/2013 3:21:46 PM

35 The first four stages of a pattern of arcs from congruent circles are shown below.180 120 Stage 1Stage 2 53.3 80 Stage 3Stage 4If this pattern continues, which expression can be used to find the degree measure of the arcin Stage n?A20(10 n2)B180C60(4 n)D 2701(n 1)32n336 In the figure below, k t and k q.ktDrBCAqBased on this information, which statement can be proved true?F ACB ABCGCABH DCB BCAJCABis an acute triangle.is a right triangle.Page 28TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 285/28/2013 3:21:46 PM

37 The main entrance to the Louvre art museum is shaped like a pyramid. The pyramid is71 feet tall and has a slant height of approximately 91 feet. Each side of the square basemeasures 115 feet.Which of the following is closest to the lateral surface area of the pyramid?A20,930 ft2B16,330 ft2C10, 465 ft2D34,155 ft2Page 29TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 295/28/2013 3:21:46 PM

38 A company is designing a flotation device made of foam. The shape of the design is modeledbelow.Which net can be folded to form the shape of the flotation device?FHGJPage 30TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 305/28/2013 3:21:47 PM

39 The diagram below shows the arcs and segments used to construct ABC, given line k.CAWBkBased on this construction, which statement is not true?A AWC is complementary to CWB.BCWB is a right triangle.CACB is isosceles.Dm CAB m CBAPage 31TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 315/28/2013 3:21:47 PM

40 Parallelogram ABCD was transformed to form parallelogram A′B′C ′D ′.yCB10987C'65B'4AD32D'1–10 –9 –8 –7 –6 –5 –4 –3 –2 –1–1–2–3–4123456789 10xA'–5–6–7–8–9–10Which rule describes the transformation that was used to form parallelogram A′B′C ′D ′?F(x, y)G( x, y)H(x 6, y)J( x, y 3)Page 32TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 325/28/2013 3:21:47 PM

41 Within a square section of land, a landscaper will build a path, as represented by the shadedsection in the diagram below.30 15 ft60 60 15 fty30 Which measure is closest to the value of y?A5.5 ftB3.1 ftC4.3 ftD 7.5 ft42 The top of a bench has a length of 5 ft and a width of 2 ft. A second bench is similar to thefirst bench. The top of the second bench is 3 ft wide. What is the length of the top of thesecond bench?F6 ftG 7 ftH 4.5 ftJ7.5 ftPage 33TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 335/28/2013 3:21:47 PM

43ABCand PQR are shown in the diagram below.B50 ARP60 CQBased on the information provided in the diagram, what is m P in degrees?Record your answer and fill in the bubbles on your answer document.44 A civil engineer is drawing a plan for the location and length of a new underground sewer pipeon a coordinate grid. The pipe on the plan will run from point N (a, 2) to point P (1, b) onthe coordinate grid. Which expression represents the shortest distance between N and P inunits?F(a 2)2 (1 b)2G(1 a)2 (b 2)2H(a2)2(1b)2J(1a)2(b2)2Page 34TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 345/28/2013 3:21:47 PM

45 In the spinner modeled below, Sector 1 has twice the area of Sector 3.1243If the arrow is spun once, what is the probability that the arrow will land in Sector 1?AB1314CD162346 A triangle is enlarged by multiplying each of its dimensions by 4. Based on this information,which of the following statements is true?FThe perimeter of the new triangle is 12 times the perimeter of the original triangle.G The perimeter of the new triangle is 16 times the perimeter of the original triangle.H The perimeter of the new triangle is 18 times the perimeter of the original triangle.JThe perimeter of the new triangle is 4 times the perimeter of the original triangle.Page 35TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 355/28/2013 3:21:47 PM

47 The slopes of the sides of quadrilateral ABCD are shown in the table below.SideSlopeAB25BC 25CDAD25 52Which statement describes the relationships between the sides of the quadrilateral?AAD is parallel to BC, but AB is not parallel to CD.BAB is parallel to CD, but AD is not parallel to BC .CAB is parallel to CD, and AD is parallel to BC .DAD is not parallel to BC, and AB is not parallel to CD.48 Two motorcycles start at the same point. One motorcycle travels 15 km due north and stops.The second motorcycle travels 32 km due west and stops. Which value is closest to thedistance between the motorcycles when they stop?F28.3 kmG 47.0 kmH 35.3 kmJ21.9 kmPage 36TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 365/28/2013 3:21:47 PM

49 A town wants to fence in a rectangular section of a park. The table shows five possible plansfor the dimensions of this fenced section. The changes in the width and the length of theseplans follow a pattern.PlanWidth(feet)Length(feet)Area(square feet)1163454421832576320306004222861652426624If six additional plans are added to the table and follow the same pattern, which conclusion isnot correct?AThe area of one of the additional plans exceeds 624 square feet.BThe area of one of the additional plans is less than 544 square feet.CThe area in Plan 6 is the same as the area in Plan 5.D The area in Plan 7 is less than the area in Plan 6.Page 37TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 375/28/2013 3:21:47 PM

50 Points A, B, C, and D are the vertices of a square. Points E and F are the centers of twocongruent semicircles that are tangent to each other at point G.y98765AD43EG2BF1–9 –8 –7 –6 –5 –4 –3 –2 9Which value is closest to the area of the shaded regions?F7.7 units2G4.3 units2H17.2 units2J64.3 units2Page 38TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 385/28/2013 3:21:47 PM

51 The diagram below represents one layout of a hexagonal swimming pool that contains a drainat point D in the center of a rectangular yard.DOther layouts are also being considered. Which layout is the result of a 90 counterclockwiserotation of the original layout using D as the center of rotation?ABDDCDDDPage 39TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 395/28/2013 3:21:48 PM

52 In DAC shown below, EB DC .A18 cmEB4.8 cmDCIf AC 28.5 cm, what is the length of AB ?F22.5 cmG 14.4 cmH 36.1 cmJ23.7 cmPage 40BE SURE YOU HAVE RECORDED ALL OF YOUR ANSWERSON THE ANSWER DOCUMENT.TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 40STOP5/28/2013 3:21:48 PM

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STAARGeometryMay 2013TX546302TX-EOC-GEOM Release-Book-May-2013 r3 052813.indd 441 2 3 4 5 A B C D EPrinted in the USADPSS/ISD61925/28/2013 3:21:48 PM

STAAR GEOMETRY REFERENCE MATERIALS. COORDINATE GEOMETRY Midpoint x x y y. 1 2 1 2. 2 2 , Distance formula d x x y y ( ) ( ) 2 1 2 2 1 2. Slope of a line. m y y x x . 2 1 2 1. Slope-intercept form of a linear equation y mx b Point-slope form of a linear equation y y mx x . 1 1 ( ) Standard form of a linear .