# 0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

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1 0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle O shown in the diagram below, chords AB and CD are parallel. 1) D ) r x-axis 3) r y-axis 4) (x, y) (x, y) If mab = 104 and mcd = 168, what is mbd? 1) 38 ) 44 3) 88 4) 96 3 As shown in the diagram below, CD is a median of ABC. Which statement is always true? 1) AD DB ) AC AD 3) ACD CDB 4) BCD ACD 5 Line segment AB is a diameter of circle O whose center has coordinates (6, 8). What are the coordinates of point B if the coordinates of point A are (4, )? 1) (1, 3) ) (5, 5) 3) (8, 14) 4) (10, 10) 6 Plane A and plane B are two distinct planes that are both perpendicular to line. Which statement about planes A and B is true? 1) Planes A and B have a common edge, which forms a line. ) Planes A and B are perpendicular to each other. 3) Planes A and B intersect each other at exactly one point. 4) Planes A and B are parallel to each other. 1

2 7 Triangle ABC is similar to triangle DEF. The lengths of the sides of ABC are 5, 8, and 11. What is the length of the shortest side of DEF if its perimeter is 60? 1) 10 ) 1.5 3) 0 4) In the diagram below of right triangle ABC, altitude CD is drawn to hypotenuse AB. 10 What is the slope of the line perpendicular to the line represented by the equation x + 4y = 1? 1) ) 3) 1 4) 1 11 Triangle ABC is shown in the diagram below. If AD = 3 and DB = 1, what is the length of altitude CD? 1) 6 ) 6 5 3) 3 4) The diagram below shows the construction of an equilateral triangle. Which statement justifies this construction? 1) A + B + C = 180 ) m A = m B = m C 3) AB = AC = BC 4) AB + BC > AC If DE joins the midpoints of ADC and AEB, which statement is not true? 1) DE = 1 CB ) DE CB AD 3) DC = DE CB 4) ABC AED 1 The equations x + y = 5 and y = 5 are graphed on a set of axes. What is the solution of this system? 1) (0, 0) ) (5, 0) 3) (0, 5) 4) (5, 5) 13 Square ABCD has vertices A(, 3), B(4, 1), C(, 5), and D( 4, 3). What is the length of a side of the square? 1) 5 ) 10 3) 4 5 4) 10

3 14 The diagram below shows ABD, with ABC, BE AD, and EBD CBD. 16 Which set of numbers could not represent the lengths of the sides of a right triangle? 1) {1, 3, 10 } ) {, 3, 4} 3) {3, 4, 5} 4) {8, 15, 17} If m ABE = 5, what is m D? 1) 6 ) 38 3) 5 4) As shown in the diagram below, FD and CB intersect at point A and ET is perpendicular to both FD and CB at A. 17 How many points are 5 units from a line and also equidistant from two points on the line? 1) 1 ) 3) 3 4) 0 18 The equation of a circle is (x ) + (y + 5) = 3. What are the coordinates of the center of this circle and the length of its radius? 1) (, 5) and 16 ) (, 5) and 16 3) (, 5) and 4 4) (, 5) and 4 19 The equation of a line is y = x + 5. What is an 3 equation of the line that is perpendicular to the given line and that passes through the point (4, )? 1) y = 3 x 3 ) y = 3 x 4 3) y = 3 x + 7 Which statement is not true? 1) ET is perpendicular to plane BAD. ) ET is perpendicular to plane FAB. 3) ET is perpendicular to plane CAD. 4) ET is perpendicular to plane BAT. 4) y = 3 x + 8 3

4 0 Consider the relationship between the two statements below. If , then In circle R shown below, diameter DE is perpendicular to chord ST at point L. If = 4 + 3, then 5 = These statements are 1) inverses ) converses 3) contrapositives 4) biconditionals 1 In the diagram of trapezoid ABCD below, AB DC, AD BC, m A = 4x + 0, and m C = 3x 15. Which statement is not always true? 1) SL TL ) RS = DR 3) RL LE 4) (DL)(LE) = (SL)(LT) What is m D? 1) 5 ) 35 3) 60 4) 90 3 Which equation represents circle A shown in the diagram below? 1) (x 4) + (y 1) = 3 ) (x + 4) + (y + 1) = 3 3) (x 4) + (y 1) = 9 4) (x + 4) + (y + 1) = 9 4

5 4 Which equation represents a line that is parallel to the line whose equation is 3x y = 7? 1) y = 3 x As shown in the diagram of rectangle ABCD below, diagonals AC and BD intersect at E. ) y = 3 x + 4 3) y = 3 x 5 4) y = 3 x 4 5 In the diagram below of circle O, PAC and PBD are secants. If mcd = 70 and mab = 0, what is the degree measure of P? 1) 5 ) 35 3) 45 4) 50 6 The measure of an interior angle of a regular polygon is 10. How many sides does the polygon have? 1) 5 ) 6 3) 3 4) 4 If AE = x + and BD = 4x 16, then the length of AC is 1) 6 ) 10 3) 1 4) 4 8 If the vertices of ABC are A(, 4), B(, 8), and C( 5, 6), then ABC is classified as 1) right ) scalene 3) isosceles 4) equilateral 9 After the transformation r y = x, the image of ABC is A B C. If AB = x + 13 and A B = 9x 8, find the value of x. 30 In the diagram below, circles A and B are tangent at point C and AB is drawn. Sketch all common tangent lines. 5

6 31 On the set of axes below, graph the locus of points 4 units from (0, 1) and the locus of points 3 units from the origin. Label with an X any points that satisfy both conditions. 33 Using a compass and straightedge, construct a line perpendicular to line through point P. [Leave all construction marks.] 3 Write an equation of a circle whose center is ( 3, ) and whose diameter is Write an equation of the line that is the perpendicular bisector of the line segment having endpoints (3, 1) and (3, 5). [The use of the grid below is optional] 6

7 35 A right circular cylinder with a height of 5 cm has a base with a diameter of 6 cm. Find the lateral area of the cylinder to the nearest hundredth of a square centimeter. Find the volume of the cylinder to the nearest hundredth of a cubic centimeter. 38 The diagram below shows rectangle ABCD with points E and F on side AB. Segments CE and DF intersect at G, and ADG BCG. Prove: AE BF 36 Triangle ABC has vertices A(5, 1), B(1, 4) and C(1, 1). State and label the coordinates of the vertices of A B C, the image of ABC, following the composite transformation T 1, 1 D. [The use of the set of axes below is optional.] 37 In ABC, m A = x + 1, m B = 11x + 5, and m C = 13x 17. Determine the longest side of ABC. 7

8 ID: A 0113ge Answer Section 1 ANS: 1 PTS: REF: ge STA: G.G.9 TOP: Triangle Congruency ANS: 360 ( ) Parallel chords intercept congruent arcs. = 44 PTS: REF: 01130ge STA: G.G.5 TOP: Chords 3 ANS: 1 PTS: REF: ge STA: G.G.4 TOP: Statements 4 ANS: 3 PTS: REF: ge STA: G.G.56 TOP: Identifying Transformations 5 ANS: 3 6 = 4 + x 4 + x = 1 x = 8. 8 = + y + y = 16 y = 14. PTS: REF: ge STA: G.G.66 TOP: Midpoint 6 ANS: 4 PTS: REF: ge STA: G.G.9 TOP: Planes 7 ANS: 5 Perimeter of DEF is = 4. 4 = x 60 4x = 300 x = 1.5 PTS: REF: ge STA: G.G.45 TOP: Similarity KEY: perimeter and area 8 ANS: 1 x = 3 1 x = 6 PTS: REF: ge STA: G.G.47 TOP: Similarity KEY: altitude 9 ANS: 3 PTS: REF: ge STA: G.G.0 TOP: Constructions 10 ANS: The slope of x + 4y = 1 is m = A B = 4 = 1. m =. PTS: REF: ge STA: G.G.6 TOP: Parallel and Perpendicular Lines 1

9 ID: A 11 ANS: 3 PTS: REF: ge STA: G.G.4 TOP: Midsegments 1 ANS: 3 x + 5 = 5 x = 0 PTS: REF: 01131ge STA: G.G.70 TOP: Quadratic-Linear Systems 13 ANS: ( 4) + ( 3 ( 1)) = 40 = 4 10 = 10 PTS: REF: ge STA: G.G.69 TOP: Quadrilaterals in the Coordinate Plane 14 ANS: = ( ) = 6 PTS: REF: ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles 15 ANS: 4 PTS: REF: ge STA: G.G.1 TOP: Planes 16 ANS: PTS: REF: ge STA: G.G.48 TOP: Pythagorean Theorem 17 ANS: PTS: REF: ge STA: G.G. TOP: Locus 18 ANS: 4 PTS: REF: ge STA: G.G.73 TOP: Equations of Circles 19 ANS: 4 m = 3. = 3 (4) + b m = 3 = 6 + b 8 = b PTS: REF: ge STA: G.G.64 TOP: Parallel and Perpendicular Lines 0 ANS: 1 PTS: REF: 01130ge STA: G.G.6 TOP: Conditional Statements 1 ANS: 3 (4x + 0) + (3x 15) = 360. D = 3(5) 15 = 60 8x x 30 = x + 10 = x = 350 x = 5 PTS: REF: 01131ge STA: G.G.40 TOP: Trapezoids

10 ID: A ANS: 3 PTS: REF: 0113ge STA: G.G.49 TOP: Chords 3 ANS: 4 PTS: REF: 01133ge STA: G.G.7 TOP: Equations of Circles 4 ANS: 3 m = A B = 3 = 3 PTS: REF: 01134ge STA: G.G.63 TOP: Parallel and Perpendicular Lines 5 ANS: = 5 PTS: REF: 01135ge STA: G.G.51 TOP: Arcs Determined by Angles KEY: outside circle 6 ANS: (n )180 = 10 n. 180n 360 = 10n 60n = 360 n = 6 PTS: REF: 01136ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons 7 ANS: 4 x 8 = x +. AE = 10 + = 1. AC = (AE) = (1) = 4 x = 10 PTS: REF: 01137ge STA: G.G.39 TOP: Special Parallelograms 8 ANS: 3 AB = 8 4 = 4. BC = ( ( 5)) + (8 6) = 13. AC = ( ( 5)) + (4 6) = 13 PTS: REF: 01138ge STA: G.G.69 TOP: Triangles in the Coordinate Plane 9 ANS: Distance is preserved after the reflection. x + 13 = 9x 8 1 = 7x 3 = x PTS: REF: 01139ge STA: G.G.55 TOP: Properties of Transformations 3

11 ID: A 30 ANS: PTS: REF: ge STA: G.G.50 TOP: Tangents KEY: common tangency 31 ANS: PTS: REF: ge STA: G.G.3 TOP: Locus 3 ANS: If r = 5, then r = 5. (x + 3) + (y ) = 5 PTS: REF: 01133ge STA: G.G.71 TOP: Equations of Circles 33 ANS: PTS: REF: ge STA: G.G.19 TOP: Constructions 34 ANS: M = 3 + 3, = (3, ). y =. PTS: REF: ge STA: G.G.68 TOP: Perpendicular Bisector 35 ANS: L = πrh = π V = πr h = π(3) (5) PTS: 4 REF: ge STA: G.G.14 TOP: Volume and Lateral Area 4

12 ID: A 36 ANS: A (11, 1), B (3, 7), C (3, 1) PTS: 4 REF: ge STA: G.G.58 TOP: Compositions of Transformations 37 ANS: x x x 17 = 180. m A = = 48 x + 4x 180 = 0 (x + 30)(x 6) = 0 x = 6 m B = 11(6) + 5 = 71 m C = 13(6) 7 = 61. B is the largest angle, so AC in the longest side. PTS: 4 REF: ge STA: G.G.34 TOP: Angle Side Relationship 38 ANS: Rectangle ABCD with points E and F on side AB, segments CE and DF intersect at G, and ADG BCE are given. AD BC because opposite sides of a rectangle are congruent. A and B are right angles and congruent because all angles of a rectangle are right and congruent. ADF BCE by ASA. AF BE per CPCTC. EF FE under the Reflexive Property. AF EF BE FE using the Subtraction Property of Segments. AE BF because of the Definition of Segments. PTS: 6 REF: ge STA: G.G.7 TOP: Quadrilateral Proofs 5

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