# 0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.

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1 0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I, II, III, and IV, are part of the construction of the perpendicular bisector of line segment AB? 1) I and II 2) I and III ) II and III 4) II and IV 2 If JKL MNO, which statement is always true? 1) KLJ NMO 2) KJL MON ) JL MO 4) JK ON The composite transformation of ABC to A B C is an example of a 1) reflection followed by a rotation 2) reflection followed by a translation ) translation followed by a rotation 4) translation followed by a reflection 1

2 4 In the diagram below of ACE, medians AD, EB, and CF intersect at G. The length of FG is 12 cm. 6 In the diagram below, line p intersects line m and line n. What is the length, in centimeters, of GC? 1) 24 2) 12 ) 6 4) 4 5 In the diagram below of circle O, chord AB is parallel to chord CD. If m 1 = 7x and m 2 = 5x + 0, lines m and n are parallel when x equals 1) ) 15 ) ) In the diagram of KLM below, m L = 70, m M = 50, and MK is extended through N. Which statement must be true? 1) AC BD 2) AB CD ) AB CD 4) ABD CDB What is the measure of LKN? 1) 60º 2) 120º ) 180º 4) 00º 2

3 8 If two distinct planes, A and B, are perpendicular to line c, then which statement is true? 1) Planes A and B are parallel to each other. 2) Planes A and B are perpendicular to each other. ) The intersection of planes A and B is a line parallel to line c. 4) The intersection of planes A and B is a line perpendicular to line c. 9 What is the length of the line segment whose endpoints are A( 1, 9) and B(7, 4)? 1) 61 2) 89 ) 205 4) 2 10 What is an equation of circle O shown in the graph below? 11 In the diagram below, parallelogram ABCD has diagonals AC and BD that intersect at point E. Which expression is not always true? 1) DAE BCE 2) DEC BEA ) AC DB 4) DE EB 12 The volume, in cubic centimeters, of a sphere whose diameter is 6 centimeters is 1) 12π 2) 6π ) 48π 4) 288π 1 The equation of line k is y = 1 x 2. The equation of line m is 2x + 6y = 18. Lines k and m are 1) parallel 2) perpendicular ) the same line 4) neither parallel nor perpendicular 1) (x + 1) 2 + (y ) 2 = 25 2) (x 1) 2 + (y + ) 2 = 25 ) (x 5) 2 + (y + 6) 2 = 25 4) (x + 5) 2 + (y 6) 2 = What are the center and the radius of the circle whose equation is (x 5) 2 + (y + ) 2 = 16? 1) ( 5, ) and 16 2) (5, ) and 16 ) ( 5, ) and 4 4) (5, ) and 4 15 Triangle ABC has vertices A(0, 0), B(, 2), and C(0, 4). The triangle may be classified as 1) equilateral 2) isosceles ) right 4) scalene

4 16 In rhombus ABCD, the diagonals AC and BD intersect at E. If AE = 5 and BE = 12, what is the length of AB? 1) 7 2) 10 ) 1 4) As shown in the diagram below, ABC DEF, AB = 7x, BC = 4, DE = 7, and EF = x. 17 In the diagram below of circle O, PA is tangent to circle O at A, and PBC is a secant with points B and C on the circle. What is the length of AB? 1) 28 2) 2 ) 14 4) 4 If PA = 8 and PB = 4, what is the length of BC? 1) 20 2) 16 ) 15 4) A man wants to place a new bird bath in his yard so that it is 0 feet from a fence, f, and also 10 feet from a light pole, P. As shown in the diagram below, the light pole is 5 feet away from the fence. 18 Lines m and n intersect at point A. Line k is perpendicular to both lines m and n at point A. Which statement must be true? 1) Lines m, n, and k are in the same plane. 2) Lines m and n are in two different planes. ) Lines m and n are perpendicular to each other. 4) Line k is perpendicular to the plane containing lines m and n. 19 In DEF, m D = x + 5, m E = 4x 15, and m F = 2x Which statement is true? 1) DF = FE 2) DE = FE ) m E = m F 4) m D = m F How many locations are possible for the bird bath? 1) 1 2) 2 ) 4) 0 4

5 22 As shown on the graph below, R S T is the image of RST under a single transformation. 26 When ABC is dilated by a scale factor of 2, its image is A B C. Which statement is true? 1) AC A C 2) A A ) perimeter of ABC = perimeter of A B C 4) 2(area of ABC) = area of A B C 27 What is the slope of a line that is perpendicular to the line whose equation is x + 5y = 4? 1) 5 2) 5 ) 5 Which transformation does this graph represent? 1) glide reflection 2) line reflection ) rotation 4) translation 4) 5 28 In the diagram below of right triangle ABC, altitude BD is drawn to hypotenuse AC, AC = 16, and CD = 7. 2 Which line is parallel to the line whose equation is 4x + y = 7 and also passes through the point ( 5, 2)? 1) 4x + y = 26 2) 4x + y = 14 ) x + 4y = 7 4) x + 4y = If the vertex angles of two isosceles triangles are congruent, then the triangles must be 1) acute 2) congruent ) right 4) similar 25 Which quadrilateral has diagonals that always bisect its angles and also bisect each other? 1) rhombus 2) rectangle ) parallelogram 4) isosceles trapezoid What is the length of BD? 1) 7 2) 4 7 ) 7 4) Given the true statement, "The medians of a triangle are concurrent," write the negation of the statement and give the truth value for the negation. 5

6 0 Using a compass and straightedge, on the diagram below of RS, construct an equilateral triangle with RS as one side. [Leave all construction marks.] 2 A pentagon is drawn on the set of axes below. If the pentagon is reflected over the y-axis, determine if this transformation is an isometry. Justify your answer. [The use of the set of axes is optional.] 1 The Parkside Packing Company needs a rectangular shipping box. The box must have a length of 11 inches and a width of 8 inches. Find, to the nearest tenth of an inch, the minimum height of the box such that the volume is at least 800 cubic inches. In the diagram below of ABC, D is a point on AB, E is a point on BC, AC DE, CE = 25 inches, AD = 18 inches, and DB = 12 inches. Find, to the nearest tenth of an inch, the length of EB. 4 In circle O, diameter RS has endpoints R(a,2b 1) and S(a 6, 4b + 5). Find the coordinates of point O, in terms of a and b. Express your answer in simplest form. 6

7 5 On the set of coordinate axes below, graph the locus of points that are equidistant from the lines y = 6 and y = 2 and also graph the locus of points that are units from the y-axis. State the coordinates of all points that satisfy both conditions. 7 Solve the following system of equations graphically. 2x 2 4x = y + 1 x + y = 1 6 In the diagram below, tangent ML and secant MNK are drawn to circle O. The ratio mln :mnk :mkl is :4:5. Find m LMK. 8 In the diagram below, PA and PB are tangent to circle O, OA and OB are radii, and OP intersects the circle at C. Prove: AOP BOP 7

8 ID: A 0611ge Answer Section 1 ANS: 2 PTS: 2 REF: ge STA: G.G.18 TOP: Constructions 2 ANS: PTS: 2 REF: ge STA: G.G.29 TOP: Triangle Congruency ANS: 4 PTS: 2 REF: 06110ge STA: G.G.60 TOP: Identifying Transformations 4 ANS: 1 PTS: 2 REF: ge STA: G.G.4 TOP: Centroid 5 ANS: 1 Parallel lines intercept congruent arcs. PTS: 2 REF: ge STA: G.G.52 TOP: Chords 6 ANS: 2 7x = 5x + 0 2x = 0 x = 15 PTS: 2 REF: ge STA: G.G.5 TOP: Parallel Lines and Transversals 7 ANS: 2 PTS: 2 REF: ge STA: G.G.2 TOP: Exterior Angle Theorem 8 ANS: 1 PTS: 2 REF: ge STA: G.G.9 TOP: Planes 9 ANS: 2 d = ( 1 7) 2 + (9 4) 2 = = 89 PTS: 2 REF: ge STA: G.G.67 TOP: Distance KEY: general 10 ANS: 1 PTS: 2 REF: ge STA: G.G.72 TOP: Equations of Circles 11 ANS: PTS: 2 REF: ge STA: G.G.8 TOP: Parallelograms 12 ANS: 2 V = 4 πr = 4 π = 6π PTS: 2 REF: ge STA: G.G.16 TOP: Volume and Surface Area 1 ANS: 1 PTS: 2 REF: 06111ge STA: G.G.6 TOP: Parallel and Perpendicular Lines 14 ANS: 4 PTS: 2 REF: ge STA: G.G.7 TOP: Equations of Circles 15 ANS: 2 PTS: 2 REF: ge STA: G.G.69 TOP: Triangles in the Coordinate Plane 1

9 ID: A 16 ANS: = 1 PTS: 2 REF: ge STA: G.G.9 TOP: Special Parallelograms 17 ANS: 4 4(x + 4) = 8 2 4x + 16 = 64 4x = 48 x = 12 PTS: 2 REF: ge STA: G.G.5 TOP: Segments Intercepted by Circle KEY: tangent and secant 18 ANS: 4 PTS: 2 REF: ge STA: G.G.1 TOP: Planes 19 ANS: 1 x x x + 10 = 180. m D = (20) + 5 = 65. m E = 4(20) 15 = 65. 9x = 180 x = 20 PTS: 2 REF: ge STA: G.G.0 TOP: Interior and Exterior Angles of Triangles 20 ANS: 7x 4 = 7. 7(2) = 14 x 7x 2 = 28 x = 2 PTS: 2 REF: ge STA: G.G.45 TOP: Similarity KEY: basic 21 ANS: 2 PTS: 2 REF: ge STA: G.G.22 TOP: Locus 22 ANS: PTS: 2 REF: ge STA: G.G.56 TOP: Identifying Transformations 2 ANS: 2 The slope of a line in standard form is A B 4, so the slope of this line is. A parallel line would also have a slope of 4. Since the answers are in standard form, use the point-slope formula. y 2 = 4 (x + 5) y 6 = 4x 20 4x + y = 14 PTS: 2 REF: 06112ge STA: G.G.65 TOP: Parallel and Perpendicular Lines 24 ANS: 4 PTS: 2 REF: ge STA: G.G.1 TOP: Isosceles Triangle Theorem 2

10 ID: A 25 ANS: 1 PTS: 2 REF: ge STA: G.G.9 TOP: Special Parallelograms 26 ANS: 2 PTS: 2 REF: ge STA: G.G.59 TOP: Properties of Transformations 27 ANS: 4 The slope of x + 5y = 4 is m = A B = 5. m = 5. PTS: 2 REF: ge STA: G.G.62 TOP: Parallel and Perpendicular Lines 28 ANS: 1 x 2 = 7(16 7) x 2 = 6 x = 9 7 x = 7 PTS: 2 REF: ge STA: G.G.47 TOP: Similarity KEY: altitude 29 ANS: The medians of a triangle are not concurrent. False. PTS: 2 REF: ge STA: G.G.24 TOP: Negations 0 ANS: PTS: 2 REF: 06110ge STA: G.G.20 TOP: Constructions 1 ANS: 9.1. (11)(8)h = 800 h 9.1 PTS: 2 REF: 06111ge STA: G.G.12 TOP: Volume

11 ID: A 2 ANS: Yes. A reflection is an isometry. PTS: 2 REF: 06112ge STA: G.G.55 TOP: Properties of Transformations ANS: x = x = 00 x 16.7 PTS: 2 REF: 0611ge STA: G.G.46 TOP: Side Splitter Theorem 4 ANS: a + a 6 2b 1 + 4b + 5 (2a, b + 2)., 2 2 = 4a 6, 6b = (2a, b + 2) PTS: 2 REF: 06114ge STA: G.G.66 TOP: Midpoint 5 ANS: PTS: 4 REF: 06115ge STA: G.G.2 TOP: Locus 6 ANS: x + 4x + 5x = 60. mln :mnk :mkl = 90:120:150. = 0 2 x = 20 PTS: 4 REF: 06116ge STA: G.G.51 TOP: Arcs Determined by Angles KEY: outside circle 4

12 ID: A 7 ANS: PTS: 4 REF: 06117ge STA: G.G.70 TOP: Quadratic-Linear Systems 8 ANS: OA OB because all radii are equal. OP OP because of the reflexive property. OA PA and OB PB because tangents to a circle are perpendicular to a radius at a point on a circle. PAO and PBO are right angles because of the definition of perpendicular. PAO PBO because all right angles are congruent. AOP BOP because of HL. AOP BOP because of CPCTC. PTS: 6 REF: 06118ge STA: G.G.27 TOP: Circle Proofs 5

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