0116geo. Geometry CCSS Regents Exam William is drawing pictures of cross sections of the right circular cone below.
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1 0116geo 1 William is drawing pictures of cross sections of the right circular cone below. 3 In parallelogram QRST shown below, diagonal is drawn, U and V are points on and, respectively, and intersects at W. Which drawing can not be a cross section of a cone? 2 An equation of a line perpendicular to the line represented by the equation passing through is and If,, and, what is? 37º 60º 72º 83º 4 A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank contains 1680 cubic inches of water. What percent of the fish tank is empty? Which transformation would result in the perimeter of a triangle being different from the perimeter of its image? 1
2 6 In the diagram below, bisects at B, and bisects at C. 8 Triangle ABC and triangle DEF are graphed on the set of axes below. Which statement is always true? bisects at C. bisects at B. 7 As shown in the diagram below, a regular pyramid has a square base whose side measures 6 inches. If the altitude of the pyramid measures 12 inches, its volume, in cubic inches, is Which sequence of transformations maps triangle ABC onto triangle DEF? a reflection over the x-axis followed by a reflection over the y-axis a 180 rotation about the origin followed by a reflection over the line a 90 clockwise rotation about the origin followed by a reflection over the y-axis a translation 8 units to the right and 1 unit up followed by a 90 counterclockwise rotation about the origin 9 In, the complement of is. Which statement is always true? 10 A line that passes through the points whose coordinates are and is dilated by a scale factor of 3 and centered at the origin. The image of the line is perpendicular to the original line is parallel to the original line passes through the origin is the original line 2
3 11 Quadrilateral ABCD is graphed on the set of axes below. 13 In the diagram below,. If and, which statement will justify similarity by SAS?,, and,, and,, and,, and When ABCD is rotated 90 in a counterclockwise direction about the origin, its image is quadrilateral A'B'C'D'. Is distance preserved under this rotation, and which coordinates are correct for the given vertex? no and no and yes and yes and 12 In the diagram below of circle O, the area of the shaded sector LOM is. 14 The diameter of a basketball is approximately 9.5 inches and the diameter of a tennis ball is approximately 2.5 inches. The volume of the basketball is about how many times greater than the volume of the tennis ball? The endpoints of one side of a regular pentagon are and. What is the perimeter of the pentagon? If the length of is 6 cm, what is? 10º 20º 40º 80º 3
4 16 In the diagram of right triangle ABC shown below, and. 20 The ratio of similarity of to is. If and, then the length of is What is the measure of , to the nearest degree? 21 In the diagram below,,,,, and are chords of circle O, is tangent at point D, and radius is drawn. Sam decides to apply this theorem to the diagram: An angle inscribed in a semi-circle is a right angle. 17 What are the coordinates of the center and length of the radius of the circle whose equation is? and 36 and 6 and 36 and 6 18 The coordinates of the vertices of are,, and. Which type of triangle is? right acute obtuse equiangular 19 Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used to make the sphere weighs.075 pound per cubic inch. If the sphere's radius is 4 inches, what is the weight of the sphere, to the nearest pound? Which angle is Sam referring to? 22 In the diagram below, is the altitude drawn to the hypotenuse of right triangle ABC. Which lengths would not produce an altitude that measures? and and and and 4
5 23 A designer needs to create perfectly circular necklaces. The necklaces each need to have a radius of 10 cm. What is the largest number of necklaces that can be made from 1000 cm of wire? In the diagram below of circle O with diameter and radius, chord is parallel to chord. 24 In shown below, points T and O are on and, respectively. Segment OT is drawn so that. If, determine and state. If,, and, what is the length of? Directed line segment PT has endpoints whose coordinates are and. Determine the coordinates of point J that divides the segment in the ratio 2 to 1. [The use of the set of axes below is optional.] 25 Triangle ABC is graphed on the set of axes below. Graph and label, the image of after a reflection over the line. 5
6 28 As graphed on the set of axes below, is the image of after a sequence of transformations. 30 During an experiment, the same type of bacteria is grown in two petri dishes. Petri dish A has a diameter of 51 mm and has approximately 40,000 bacteria after 1 hour. Petri dish B has a diameter of 75 mm and has approximately 72,000 bacteria after 1 hour. Is congruent to? Use the properties of rigid motion to explain your answer. 29 A carpenter leans an extension ladder against a house to reach the bottom of a window 30 feet above the ground. As shown in the diagram below, the ladder makes a 70 angle with the ground. To the nearest foot, determine and state the length of the ladder. Determine and state which petri dish has the greater population density of bacteria at the end of the first hour. 31 Line is mapped onto line m by a dilation centered at the origin with a scale factor of 2. The equation of line is. Determine and state an equation for line m. 32 The aspect ratio (the ratio of screen width to height) of a rectangular flat-screen television is. The length of the diagonal of the screen is the television's screen size. Determine and state, to the nearest inch, the screen size (diagonal) of this flat-screen television with a screen height of 20.6 inches. 6
7 33 Given the theorem, The sum of the measures of the interior angles of a triangle is 180, complete the proof for this theorem. Given: Prove: Fill in the missing reasons below. 7
8 34 Triangle XYZ is shown below. Using a compass and straightedge, on the line below, construct and label, such that. [Leave all construction marks.] Based on your construction, state the theorem that justifies why is congruent to. 36 Cathy wants to determine the height of the flagpole shown in the diagram below. She uses a survey instrument to measure the angle of elevation to the top of the flagpole, and determines it to be She walks 8 meters closer and determines the new measure of the angle of elevation to be At each measurement, the survey instrument is 1.7 meters above the ground. Determine and state, to the nearest tenth of a meter, the height of the flagpole. 35 Given: Parallelogram ANDR with and bisecting and at points W and E, respectively Prove that. Prove that quadrilateral AWDE is a parallelogram. 8
1 William is drawing pictures of cross sections of the right circular cone below.
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Use this space for computations. 3 In parallelogram QRST shown below, diagonal TR. is drawn, U and V are points on TS and QR,
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