# 0811ge. Geometry Regents Exam

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1 0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation of T, 5, which line segment is parallel to P Q? 1) R Q ) R S 3) T S 4) T P 5 In the diagram below of PAO, AP is tangent to circle O at point A, OB = 7, and BP = 18. Which statement must be true? 1) C Y ) A X 3) AC YZ 4) CB XZ 3 In the diagram below of ABC, TV BC, AT = 5, TB = 7, and AV = 10. What is the length of AP? 1) 10 ) 1 3) 17 4) 4 What is the length of VC? 1) 3 1 ) ) 14 4) 4 1

2 6 A straightedge and compass were used to create the construction below. Arc EF was drawn from point B, and arcs with equal radii were drawn from E and F. 9 In the diagram below, lines n and m are cut by transversals p and q. Which statement is false? 1) m ABD = m DBC 1 ) (m ABC) = m ABD 3) (m DBC) = m ABC 4) (m ABC) = m CBD 7 What is the length of the line segment whose endpoints are (1, 4) and (9, )? 1) 5 ) 17 3) 10 4) 6 8 What is the image of the point (, 3) after the transformation r y axis? 1) (, 3) ) (, 3) 3) (, 3) 4) ( 3, ) What value of x would make lines n and m parallel? 1) 110 ) 80 3) 70 4) What is an equation of the circle with a radius of 5 and center at (1, 4)? 1) (x + 1) + (y 4) = 5 ) (x 1) + (y + 4) = 5 3) (x + 1) + (y 4) = 5 4) (x 1) + (y + 4) = 5 11 In the diagram below of BCD, side DB is extended to point A. Which statement must be true? 1) m C > m D ) m ABC < m D 3) m ABC > m C 4) m ABC > m C + m D

3 1 Which equation represents the line parallel to the line whose equation is 4x + y = 14 and passing through the point (, )? 1) y = x ) y = x In the diagram below, AB is perpendicular to plane AEFG. 3) y = 1 x 4) y = 1 x The coordinates of point A are ( 3a,4b). If point A' is the image of point A reflected over the line y = x, the coordinates of A' are 1) (4b, 3a) ) (3a, 4b) 3) ( 3a, 4b) 4) ( 4b, 3a) 14 As shown in the diagram below, AC bisects BAD and B D. Which plane must be perpendicular to plane AEFG? 1) ABCE ) BCDH 3) CDFE 4) HDFG 17 How many points are both 4 units from the origin and also units from the line y = 4? 1) 1 ) 3) 3 4) 4 Which method could be used to prove ABC ADC? 1) SSS ) AAA 3) SAS 4) AAS 15 Segment AB is the diameter of circle M. The coordinates of A are ( 4, 3). The coordinates of M are (1, 5). What are the coordinates of B? 1) (6, 7) ) (5, 8) 3) ( 3, 8) 4) ( 5, ) 18 When solved graphically, what is the solution to the following system of equations? y = x 4x + 6 1) (1, 4) ) (4, 6) 3) (1, 3) and (4, 6) 4) (3, 1) and (6, 4) y = x + 19 Triangle PQR has angles in the ratio of :3:5. Which type of triangle is PQR? 1) acute ) isosceles 3) obtuse 4) right 3

4 0 Plane A is parallel to plane B. Plane C intersects plane A in line m and intersects plane B in line n. Lines m and n are 1) intersecting ) parallel 3) perpendicular 4) skew 4 In the diagram below of circle O, diameter AOB is perpendicular to chord CD at point E, OA = 6, and OE =. 1 The diagonals of a quadrilateral are congruent but do not bisect each other. This quadrilateral is 1) an isosceles trapezoid ) a parallelogram 3) a rectangle 4) a rhombus What is the slope of a line that is perpendicular to the line represented by the equation x + y = 3? 1) ) 3) 1 4) 1 3 A packing carton in the shape of a triangular prism is shown in the diagram below. What is the length of CE? 1) 4 3 ) 3 3) 8 4) 4 5 What is the measure of each interior angle of a regular hexagon? 1) 60 ) 10 3) 135 4) 70 6 Which equation represents the perpendicular bisector of AB whose endpoints are A(8, ) and B(0, 6)? 1) y = x 4 ) y = 1 x + What is the volume, in cubic inches, of this carton? 1) 0 ) 60 3) 10 4) 40 3) y = 1 x + 6 4) y = x 1 4

5 7 As shown in the diagram below, a kite needs a vertical and a horizontal support bar attached at opposite corners. The upper edges of the kite are 7 inches, the side edges are x inches, and the vertical support bar is (x + 1) inches. 9 In the diagram below, trapezoid ABCD, with bases AB and DC, is inscribed in circle O, with diameter DC. If mab=80, find mbc. 30 On the diagram of ABC shown below, use a compass and straightedge to construct the perpendicular bisector of AC. [Leave all construction marks.] What is the measure, in inches, of the vertical support bar? 1) 3 ) 4 3) 5 4) 6 8 Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must have perpendicular diagonals? 1) the rhombus, only ) the rectangle and the square 3) the rhombus and the square 4) the rectangle, the rhombus, and the square 31 A sphere has a diameter of 18 meters. Find the volume of the sphere, in cubic meters, in terms of π. 5

6 3 Write an equation of the circle graphed in the diagram below. 34 Triangle ABC has vertices A(3, 3), B(7, 9), and C(11, 3). Determine the point of intersection of the medians, and state its coordinates. [The use of the set of axes below is optional.] 33 The diagram below shows ABC, with AEB, ADC, and ACB AED. Prove that ABC is similar to ADE. 35 In the diagram below of GJK, H is a point on GJ, HJ JK, m G = 8, and m GJK = 70. Determine whether GHK is an isosceles triangle and justify your answer. 6

7 36 As shown on the set of axes below, GHS has vertices G(3, 1), H(5, 3), and S(1, 4). Graph and state the coordinates of G H S, the image of GHS after the transformation T 3, 1 D. 38 Given: ABC with vertices A( 6, ), B(, 8), and C(6, ). AB has midpoint D, BC has midpoint E, and AC has midpoint F. Prove: ADEF is a parallelogram ADEF is not a rhombus [The use of the grid is optional.] 37 In the diagram below, ABC DEF, DE = 4, AB = x, AC = x +, and DF = x + 6. Determine the length of AB. [Only an algebraic solution can receive full credit.] 7

8 ID: A 0811ge Answer Section 1 ANS: 4 PTS: REF: ge STA: G.G.5 TOP: Compound Statements KEY: conjunction ANS: PTS: REF: 08110ge STA: G.G.9 TOP: Triangle Congruency 3 ANS: = 10 x 5x = 70 x = 14 PTS: REF: ge STA: G.G.46 TOP: Side Splitter Theorem 4 ANS: 3 PTS: REF: ge STA: G.G.55 TOP: Properties of Transformations 5 ANS: = 4 PTS: REF: ge STA: G.G.50 TOP: Tangents KEY: point of tangency 6 ANS: 4 PTS: REF: ge STA: G.G.17 TOP: Constructions 7 ANS: 3 d = (1 9) + ( 4 ) = = 100 = 10 PTS: REF: ge STA: G.G.67 TOP: Distance KEY: general 8 ANS: PTS: REF: ge STA: G.G.54 TOP: Reflections KEY: basic 9 ANS: 3 7x = 5x + 30 x = 30 x = 15 PTS: REF: ge STA: G.G.35 TOP: Parallel Lines and Transversals 10 ANS: 4 PTS: REF: ge STA: G.G.71 TOP: Equations of Circles 11 ANS: 3 PTS: REF: ge STA: G.G.3 TOP: Exterior Angle Theorem 1

9 ID: A 1 ANS: m = A B = 4 = y = mx + b = () + b 6 = b PTS: REF: 08111ge STA: G.G.65 TOP: Parallel and Perpendicular Lines 13 ANS: 1 PTS: REF: ge STA: G.G.54 TOP: Reflections KEY: basic 14 ANS: 4 PTS: REF: ge STA: G.G.8 TOP: Triangle Congruency 15 ANS: 1 1 = 4 + x 4 + x = x = 6. 5 = 3 + y 3 + y = 10 y = 7. PTS: REF: ge STA: G.G.66 TOP: Midpoint 16 ANS: 1 PTS: REF: ge STA: G.G.7 TOP: Planes 17 ANS: PTS: REF: ge STA: G.G.3 TOP: Locus 18 ANS: 3 PTS: REF: ge STA: G.G.70 TOP: Quadratic-Linear Systems 19 ANS: = PTS: REF: ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles 0 ANS: PTS: REF: 08110ge STA: G.G.8 TOP: Planes

10 ID: A 1 ANS: 1 PTS: REF: 08111ge STA: G.G.39 TOP: Special Parallelograms ANS: The slope of x + y = 3 is m = A B = 1. m =. PTS: REF: 0811ge STA: G.G.6 TOP: Parallel and Perpendicular Lines 3 ANS: 3 PTS: REF: 08113ge STA: G.G.1 TOP: Volume 4 ANS: 4 6 = 3 = 16 = 4 PTS: REF: 08114ge STA: G.G.49 TOP: Chords 5 ANS: (n )180 = (6 )180 = = 10. PTS: REF: 08115ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons 6 ANS: m =, + 6 = (4, 4) 6 m = 0 8 = 4 8 = 1 m = y = mx + b 4 = (4) + b 4 = b PTS: REF: 08116ge STA: G.G.68 TOP: Perpendicular Bisector 7 ANS: 3 x + 7 = (x + 1) x + 1 = 5 x + 49 = x + x = x 4 = x PTS: REF: 08117ge STA: G.G.48 TOP: Pythagorean Theorem 8 ANS: 3 PTS: REF: 08118ge STA: G.G.39 TOP: Special Parallelograms 9 ANS: = 50 PTS: REF: 08119ge STA: G.G.5 TOP: Chords 3

11 ID: A 30 ANS: PTS: REF: ge STA: G.G.18 TOP: Constructions 31 ANS: V = 4 3 π 93 = 97π PTS: REF: ge STA: G.G.16 TOP: Volume and Surface Area 3 ANS: (x 5) + (y + 4) = 36 PTS: REF: 08113ge STA: G.G.7 TOP: Equations of Circles 33 ANS: ACB AED is given. A A because of the reflexive property. Therefore ABC ADE because of AA. PTS: REF: ge STA: G.G.44 TOP: Similarity Proofs 34 ANS: (7, 5) m AB = 3 + 7, = (5, 6) m BC = , = (9, 6) PTS: REF: ge STA: G.G.1 TOP: Centroid, Orthocenter, Incenter and Circumcenter 4

12 ID: A 35 ANS: No, KGH is not congruent to GKH. PTS: REF: ge STA: G.G.31 TOP: Isosceles Triangle Theorem 36 ANS: G (3, 3), H (7, 7), S ( 1, 9) PTS: 4 REF: ge STA: G.G.58 TOP: Compositions of Transformations 37 ANS: x + = x + 6 x 4 x + 6x = 4x + 8 x + x 8 = 0 (x + 4)(x ) = 0 x = PTS: 4 REF: ge STA: G.G.45 TOP: Similarity KEY: basic 38 ANS: 6 + m AB =, + 8 = D(, 3) m BC = + 6, 8 + = E(4, 3) F(0, ). To prove that ADEF is a parallelogram, show that both pairs of opposite sides of the parallelogram are parallel by showing the opposite sides have the same slope: m AD = 3 6 = 5 4 AF DE because all horizontal lines have the same slope. ADEF m FE = = 5 4 is not a rhombus because not all sides are congruent. AD = = 41 AF = 6 PTS: 6 REF: ge STA: G.G.69 TOP: Quadrilaterals in the Coordinate Plane 5

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