# 0116ge. Geometry Regents Exam RT and SU intersect at O.

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1 Geometry Regents Exam 06 06ge What is the equation of a circle with its center at (5, ) and a radius of 3? ) (x 5) + (y + ) = 3 ) (x 5) + (y + ) = 9 3) (x + 5) + (y ) = 3 4) (x + 5) + (y ) = 9 In the diagram below, ABC is inscribed in circle O. 4 How many points are 3 units from the origin and also equidistant from both the x-axis and y-axis? ) ) 3) 0 4) 4 5 The converse of the statement If a triangle has one right angle, the triangle has two acute angles is ) If a triangle has two acute angles, the triangle has one right angle. ) If a triangle has one right angle, the triangle does not have two acute angles. 3) If a triangle does not have one right angle, the triangle does not have two acute angles. 4) If a triangle does not have two acute angles, the triangle does not have one right angle. The ratio of the measure of ABC to the measure of AC is ) : ) : 3) : 3 4) : 4 3 In the diagram below of rectangle RSTU, diagonals RT and SU intersect at O. 6 The surface area of a sphere is 304π square inches. The length of a radius of the sphere, in inches, is ) ) 4 3) 88 4) As shown in the diagram below of ABC, BC is extended through D, m A = 70, and m ACD = 5. If RT = 6x + 4 and SO = 7x 6, what is the length of US? ) 8 ) 3) 6 4) 3 Which statement is true? ) AC > AB ) AB > BC 3) BC < AC 4) AC < AB

2 Geometry Regents Exam 06 8 In trapezoid LMNO below, median PQ is drawn. As shown in the diagram below, M, R, and T are midpoints of the sides of ABC. If LM = x + 7, ON = 3x +, and PQ = 5, what is the value of x? ).75 ) 3.5 3) 8 4) 7 9 Points A and B are on line. How many points are 3 units from line and also equidistant from A and B? ) ) 3) 3 4) 4 If AB = 8, AC = 4, and BC = 0, what is the perimeter of quadrilateral ACRM? ) 35 ) 3 3) 4 4) In the diagram below, ABC DEFG. Transversal BHE and line segment HF are drawn. 0 The lines whose equations are x + 3y = 4 and y = mx + 6 will be perpendicular when m is ) 3 ) 3 3) 3 4) 3 If m HFG = 30 and m EHF = 70, what is m ABE? ) 40 ) 50 3) 60 4) 70 3 The graphs of the lines represented by the equations y = 3 x + 7 and y = 3 x are ) parallel ) horizontal 3) perpendicular 4) intersecting, but not perpendicular

3 Geometry Regents Exam 06 4 Which graph represents a circle whose equation is (x + 3) + (y ) = 4? 6 In circle O shown below, chord AB and diameter CD are parallel, and chords AD and BC intersect at point E. ) ) 3) 4) Which statement is false? ) AC BD ) BE = CE 3) ABE CDE 4) B C 7 When the transformation T, is performed on point A, its image is point A'( 3,4). What are the coordinates of A? ) (5, 5) ) ( 5,5) 3) (,3) 4) ( 6, 4) 8 If the sum of the interior angles of a polygon is 440, then the polygon must be ) an octagon ) a decagon 3) a hexagon 4) a nonagon 5 In ABC, m CAB = x and m ACB = x If AB is extended through point B to point D, m CBD = 5x 50. What is the value of x? ) 5 ) 30 3) 40 4) 46 3

4 Geometry Regents Exam 06 9 In ABC shown below, medians AD, BE, and CF intersect at point R. 3 A right circular cone has a diameter of 0 and a height of. What is the volume of the cone in terms of π? ) 00π ) 600π 3) 800π 4) 400π 4 Which statement is not always true when ABC XYZ. ) BC YZ ) CA XY 3) CAB ZXY 4) BCA YZX If CR = 4 and RF = x 6, what is the value of x? ) 9 ) 3) 5 4) 7 0 Which equation represents a line that passes through the point (,6) and is parallel to the line whose equation is 3x 4y = 6? ) 3x + 4y = 8 ) 4x + 3y = 0 3) 3x + 4y = 30 4) 4x + 3y = 6 5 If two sides of a triangle have lengths of 4 and 5, which fraction can not be the length of the third side? ) 9 ) 8 3) 3 4) The bases of a right prism are triangles in which MNP RST. If MP = 9, MR = 8, and MN =, what is the length of NS? ) 9 ) 3) 5 4) 8 Triangle ABC has the coordinates A(3,0), B(3,8), and C(6,6). If ABC is reflected over the line y = x, which statement is true about the image of ABC? ) One point remains fixed. ) The size of the triangle changes. 3) The orientation does not change. 4) One side of ABC is parallel to the line y = x. 4

5 Geometry Regents Exam 06 6 In the diagram below of ABC, CDA, CEB, DE AB, DE = 4, AB = 0, CD = x, and DA = x In the construction shown below, CD is drawn. What is the value of x? ) 0.5 ) 3) 5.5 4) 6 7 Given: AE bisects BD at C AB and DE are drawn ABC EDC In ABC, CD is the ) perpendicular bisector of side AB ) median to side AB 3) altitude to side AB 4) bisector of ACB 9 The sides of a triangle measure 7, 4, and 9. If the longest side of a similar triangle measures 36, determine and state the length of the shortest side of this triangle. Which statement is needed to prove ABC EDC using ASA? ) ABC and EDC are right angles. ) BD bisects AE at C. 3) BCA DCE 4) DEC BAC 5

6 Geometry Regents Exam Triangle ABC has coordinates A(6, 4), B(0,), and C(6,). On the set of axes below, graph and label A B C, the image of ABC after a dilation of. 34 Using a compass and a straightedge, construct the bisector of CDE. [Leave all construction marks.] 3 In parallelogram RSTU, m R = 5x and m S = 3x + 0. Determine and state the value of x. 35 The coordinates of ABC, shown on the graph below, are A(,5), B(5,7), and C(4,). Graph and label A' B C, the image of ABC after it is reflected over the y-axis. Graph and label A B C, the image of A B C after it is reflected over the x-axis. State a single transformation that will map ABC onto A B C. 3 Determine and state the length of a line segment whose endpoints are (6,4) and ( 9, 4). 33 The base of a right pentagonal prism has an area of 0 square inches. If the prism has an altitude of 8 inches, determine and state the volume of the prism, in cubic inches. 6

7 Geometry Regents Exam On the set of axes below, solve the following system of equations graphically and state the coordinates of all points in the solution. y = x + 4x + y x = 5 37 Given: Triangle RST has coordinates R(,7), S(3, ), and T(9,) Prove: RST is a right triangle [The use of the set of axes below is optional.] 38 In right triangle FGH shown below, m GHF = 90, altitude HJ is drawn to FG, FJ = 6, and HG = 5. Determine and state the length of JG. Determine and state the length of HJ. [Only algebraic solutions can receive full credit.] 7

8 ID: A 06ge Answer Section ANS: PTS: REF: 060ge STA: G.G.7 TOP: Equations of Circles ANS: PTS: REF: 060ge STA: G.G.5 TOP: Arcs Determined by Angles KEY: inscribed 3 ANS: 3 6x + 4 = (7x 6) US = 6() + 4 = 6 6x + 4 = 4x 6 = 8x x = PTS: REF: 0603ge STA: G.G.39 TOP: Special Parallelograms 4 ANS: 4 PTS: REF: 0604ge STA: G.G.3 TOP: Locus 5 ANS: PTS: REF: 0605ge STA: G.G.6 TOP: Converse and Biconditional 6 ANS: 304π = 4πr 576 = r 4 = r PTS: REF: 0606ge STA: G.G.6 TOP: Volume and Surface Area 7 ANS: 4 PTS: REF: 0607ge STA: G.G.34 TOP: Angle Side Relationship 8 ANS: 3 x x + = 5 4x + 8 = 50 4x = 3 x = 8 PTS: REF: 0608ge STA: G.G.40 TOP: Trapezoids 9 ANS: PTS: REF: 0609ge STA: G.G. TOP: Locus 0 ANS: 3 m = A B = 3 m = 3 PTS: REF: 060ge STA: G.G.6 TOP: Parallel and Perpendicular Lines

9 ID: A ANS: = 35 PTS: REF: 06ge STA: G.G.4 TOP: Midsegments ANS: 3 PTS: REF: 06ge STA: G.G.35 TOP: Parallel Lines and Transversals 3 ANS: 4 PTS: REF: 063ge STA: G.G.63 TOP: Parallel and Perpendicular Lines 4 ANS: PTS: REF: 064ge STA: G.G.74 TOP: Graphing Circles 5 ANS: 3 x + x + 30 = 5x = x x = 40 PTS: REF: 065ge STA: G.G.3 TOP: Exterior Angle Theorem 6 ANS: PTS: REF: 066ge STA: G.G.5 TOP: Chords and Secants 7 ANS: PTS: REF: 067ge STA: G.G.54 TOP: Translations 8 ANS: (n )80 = 440 n = 8 n = 0 PTS: REF: 068ge STA: G.G.36 TOP: Interior and Exterior Angles of Polygons 9 ANS: (x 6) = 4 x 6 = x = 8 x = 9 PTS: REF: 069ge STA: G.G.43 TOP: Centroid

10 ID: A 0 ANS: 3 m = A B = 3 4 = = 3 4 ( ) + b = 3 + b 5 = b y = 3 4 x + 5 4y = 3x x + 4y = 30 PTS: REF: 060ge STA: G.G.65 TOP: Parallel and Perpendicular Lines ANS: 4 PTS: REF: 06ge STA: G.G.0 TOP: Solids ANS: C(6,6) remains fixed after the reflection. PTS: REF: 06ge STA: G.G.55 TOP: Properties of Transformations 3 ANS: V = 3 π 5 = 00π PTS: REF: 063ge STA: G.G.5 TOP: Volume and Lateral Area 4 ANS: PTS: REF: 064ge STA: G.G.9 TOP: Triangle Congruency 5 ANS: = = < s < 9 0 > 9 0 PTS: REF: 065ge STA: G.G.33 TOP: Triangle Inequality Theorem 6 ANS: 4 x 4 = x + x x = 8x + x = x = 6 PTS: REF: 066ge STA: G.G.46 TOP: Side Splitter Theorem 7 ANS: 3 PTS: REF: 067ge STA: G.G.8 TOP: Triangle Congruency 8 ANS: PTS: REF: 068ge STA: G.G.8 TOP: Constructions 3

11 ID: A 9 ANS: 9 36 = 4 x 9x = 44 x = 6 PTS: REF: 069ge STA: G.G.45 TOP: Similarity KEY: basic 30 ANS: PTS: REF: 0630ge STA: G.G.58 TOP: Dilations 3 ANS: 5x + 3x + 0 = 80 8x + 8 = 80 8x = 7 x =.5 PTS: 4 REF: 063ge STA: G.G.38 TOP: Parallelograms 3 ANS: (6 9) + (4 4) = = 89 = 7 PTS: REF: 063ge STA: G.G.67 TOP: Distance 33 ANS: V = 0 8 = 60 PTS: REF: 0633ge STA: G.G. TOP: Volume 4

12 ID: A 34 ANS: PTS: REF: 0634ge STA: G.G.7 TOP: Constructions 35 ANS: R 80 PTS: 4 REF: 0635ge STA: G.G.58 TOP: Compositions of Transformations KEY: grids 36 ANS: PTS: 4 REF: 0636ge STA: G.G.70 TOP: Quadratic-Linear Systems 5

13 ID: A 37 ANS: PTS: 4 REF: 0638ge STA: G.G.69 TOP: Triangles in the Coordinate Plane 38 ANS: x(x + 6) = 5 y = 6 9 x + 6x 5 = 0 (x + 5)(x 9) = 0 x = 9 y = 44 y = PTS: 6 REF: 0638ge STA: G.G.47 TOP: Similarity KEY: leg 6

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