0613ge. Geometry Regents Exam 0613
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1 wwwjmaporg 0613ge 1 In trapezoid RSTV with bases and, diagonals and intersect at Q If trapezoid RSTV is not isosceles, which triangle is equal in area to? 2 In the diagram below, 3 In a park, two straight paths intersect The city wants to install lampposts that are both equidistant from each path and also 15 feet from the intersection of the paths How many lampposts are needed? What are the coordinates of, the image of, after a rotation of 180º about the origin? 5 Based on the construction below, which conclusion is not always true? Which statement can not be proven? 1
2 wwwjmaporg 6 Which equation represents the circle whose center is and that passes through the point? 9 What is the equation for circle O shown in the graph below? 7 As shown in the diagram below, when right triangle DAB is reflected over the x-axis, its image is triangle DCB Which statement justifies why? Distance is preserved under reflection Orientation is preserved under reflection Points on the line of reflection remain invariant Right angles remain congruent under reflection 10 Point A is on line m How many distinct planes will be perpendicular to line m and pass through point A? one two zero infinite 8 In,,, and Which type of triangle is? right scalene isosceles equilateral 2
3 wwwjmaporg 11 In, D is the midpoint of and E is the midpoint of If and, what is the value of x? 13 Which graph could be used to find the solution to the following system of equations? What are the coordinates of the center of a circle if the endpoints of its diameter are and? 3
4 wwwjmaporg 14 What is the converse of If an angle measures 90 degrees, then it is a right angle? If an angle is a right angle, then it measures 90 degrees An angle is a right angle if it measures 90 degrees If an angle is not a right angle, then it does not measure 90 degrees If an angle does not measure 90 degrees, then it is not a right angle 16 What is the equation of a line passing through the point and parallel to the line whose equation is? 15 As shown in the diagram below, a right pyramid has a square base, ABCD, and is the slant height 17 The volume of a sphere is approximately cubic centimeters What is the radius of the sphere, to the nearest tenth of a centimeter? Points and lie on Points and lie on Which statement is true? Which statement is not true? is isosceles and are the same line and intersect, but are not perpendicular 4
5 wwwjmaporg 19 Which set of equations represents two circles that have the same center? and and 22 Circle O with and is shown in the diagram below and and 20 Transversal intersects and, as shown in the diagram below What is the ratio of to? Which statement could always be used to prove? and are supplementary and are supplementary 21 In,,, and Which inequality is true? 23 A rectangular prism has a base with a length of 25, a width of 9, and a height of 12 A second prism has a square base with a side of 15 If the volumes of the two prisms are equal, what is the height of the second prism? In triangles ABC and DEF,,,,, and Which method could be used to prove? AA SAS SSS ASA 5
6 wwwjmaporg 25 Which graph represents a circle whose equation is? 27 In right triangle ABC shown in the diagram below, altitude is drawn to hypotenuse,, and What is the length of? Secants and are drawn to circle O from an external point, J If,, and, what is the length of? A right circular cylinder has a height of 7 inches and the base has a diameter of 6 inches Determine the lateral area, in square inches, of the cylinder in terms of 26 What is the perimeter of a rhombus whose diagonals are 16 and 30? Determine, in degrees, the measure of each interior angle of a regular octagon 6
7 wwwjmaporg 31 Triangle ABC has vertices at,, and form Find the length of in simplest radical 33 On the set of axes below, graph the locus of points 4 units from the x-axis and equidistant from the points whose coordinates are and Mark with an X all points that satisfy both conditions 32 On the ray drawn below, using a compass and straightedge, construct an equilateral triangle with a vertex at R The length of a side of the triangle must be equal to a length of the diagonal of rectangle ABCD 34 The coordinates of two vertices of square ABCD are and Determine the slope of side 7
8 wwwjmaporg 35 The coordinates of the vertices of parallelogram SWAN are,,, and State and label the coordinates of parallelogram, the image of SWAN after the transformation [The use of the set of 36 In circle O shown below, chords and and radius are drawn, such that,,,,, and axes below is optional] Determine the length of of Determine the length 37 If,,, and, find [Only an algebraic solution can receive full credit] 38 In the diagram of below, and medians and are drawn Prove: 8
9 ID: A 0613ge Answer Section 1 ANS: 2 Isosceles or not, and have a common base, and since and are bases, congruent altitudes PTS: 2 REF: ge STA: GG40 TOP: Trapezoids 2 ANS: 2 ( is true because of vertical angles ( and ( are true because CPCTC PTS: 2 REF: ge STA: GG24 TOP: Statements 3 ANS: 4 PTS: 2 REF: ge STA: GG22 TOP: Locus 4 ANS: 4 PTS: 2 REF: ge STA: GG54 TOP: Rotations 5 ANS: 2 PTS: 2 REF: ge STA: GG18 TOP: Constructions 6 ANS: 3 PTS: 2 REF: ge STA: GG71 TOP: Equations of Circles 7 ANS: 1 PTS: 2 REF: ge STA: GG55 TOP: Properties of Transformations 8 ANS: 3 PTS: 2 REF: ge STA: GG30 TOP: Interior and Exterior Angles of Triangles 9 ANS: 3 PTS: 2 REF: ge STA: GG72 TOP: Equations of Circles 10 ANS: 1 PTS: 2 REF: ge STA: GG2 TOP: Planes 11 ANS: 3 PTS: 2 REF: ge STA: GG42 TOP: Midsegments 12 ANS: 2 PTS: 2 REF: ge STA: GG66 TOP: Midpoint 1
10 ID: A 13 ANS: 2 PTS: 2 REF: ge STA: GG70 TOP: Quadratic-Linear Systems 14 ANS: 1 PTS: 2 REF: ge STA: GG26 TOP: Converse and Biconditional 15 ANS: 2 PTS: 2 REF: ge STA: GG13 TOP: Classifying Solids 16 ANS: 3 PTS: 2 REF: ge STA: GG65 TOP: Parallel and Perpendicular Lines 17 ANS: 1 PTS: 2 REF: ge STA: GG16 TOP: Volume and Surface Area 18 ANS: 4 PTS: 2 REF: ge STA: GG63 TOP: Parallel and Perpendicular Lines 19 ANS: 4 PTS: 2 REF: ge STA: GG73 TOP: Equations of Circles 20 ANS: 3 PTS: 2 REF: ge STA: GG35 TOP: Parallel Lines and Transversals 21 ANS: 2 PTS: 2 REF: ge STA: GG34 TOP: Angle Side Relationship 22 ANS: 2 PTS: 2 REF: ge STA: GG51 TOP: Arcs Determined by Angles KEY: inscribed 23 ANS: 3 PTS: 2 REF: ge STA: GG11 TOP: Volume 24 ANS: 2 PTS: 2 REF: ge STA: GG44 TOP: Similarity Proofs 25 ANS: 1 PTS: 2 REF: ge STA: GG74 TOP: Graphing Circles 2
11 ID: A 26 ANS: 2 PTS: 2 REF: ge STA: GG39 TOP: Special Parallelograms 27 ANS: 3 PTS: 2 REF: ge STA: GG47 TOP: Similarity KEY: altitude 28 ANS: 1 PTS: 2 REF: ge STA: GG53 TOP: Segments Intercepted by Circle KEY: two secants 29 ANS: PTS: 2 REF: ge STA: GG14 TOP: Volume 30 ANS: PTS: 2 REF: ge STA: GG37 TOP: Interior and Exterior Angles of Polygons 31 ANS: PTS: 2 REF: ge STA: GG69 TOP: Triangles in the Coordinate Plane 32 ANS: PTS: 2 REF: ge STA: GG20 TOP: Constructions 3
12 ID: A 33 ANS: PTS: 2 REF: ge STA: GG23 TOP: Locus 34 ANS: PTS: 4 REF: ge STA: GG69 TOP: Quadrilaterals in the Coordinate Plane 35 ANS:,,, and PTS: 4 REF: ge STA: GG58 TOP: Compositions of Transformations KEY: grids 36 ANS: PTS: 4 REF: ge STA: GG49 TOP: Chords 37 ANS: PTS: 4 REF: ge STA: GG45 TOP: Similarity KEY: basic 4
13 ID: A 38 ANS:, and medians and are given (reflexive property) is an isosceles triangle (definition of isosceles triangle) (isosceles triangle theorem) B is the midpoint of and T is the midpoint of (definition of median) and (definition of midpoint) (multiplication postulate) (SAS) (CPCTC) PTS: 6 REF: ge STA: GG27 TOP: Triangle Proofs 5
1) AB CD 2) AB = CD 3) AE = EB 4) CE = DE
1 In trapezoid RSTV with bases RS and VT, diagonals RT and SV intersect at Q. If trapezoid RSTV is not isosceles, which triangle is equal in area to RSV? 1) RQV 2) RST 3) RVT 4) SVT 2 In the diagram below,
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