END OF COURSE GEOMETRY CORE 1

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1 SESSION: 24 PE: 1 5/5/04 13:29 OIN IS-glenn VIRINI STNRS O ERNIN SSESSMENTS Spring 2004 Released Test EN O OURSE EOMETRY ORE 1 Property of the Virginia epartment of Education 2004 by the ommonwealth of Virginia epartment of Education, ames Monroe uilding, 101 N. 14th Street, Richmond, Virginia, ll rights reserved. Except as permitted by law, this material may not be reproduced or used in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage or retrieval system, without written permission from the copyright owner. ommonwealth of Virginia public school educators may photocopy or print any portion of these Released Tests for educational purposes without requesting permission. ll others should direct their requests to the ommonwealth of Virginia epartment of Education at (804) , ivision of ssessment and Reporting.

2 SESSION: 23 PE: 2 5/4/04 15:40 OIN IS-glenn eometry IRETIONS Read and solve each question. Then mark the space on the answer sheet for the best answer. SMPE If is similar to E, then :?:E. Which replaces the? to make the statement true? E 2 If 3 Y, which of the following must be true? W W Y WX is perpendicular to XY W 2 X ine l is parallel to YW Y l Y rtodes Y R1 E E Y plumber bent a flexible joint into a 136 angle, as shown. e then attached another pipe so that,, and lay on a straight line. rtodes Y R1 136 What is the value of x? ommonwealth of Virginia epartment of Education 2

3 SESSION: 23 PE: 3 5/4/04 15:40 OIN IS-glenn 3 Which pair of angles is supplementary? 4 In the figure, line t is a transversal for lines l and m. Y t Y rtodes Y R1 Y R2 Y R3 Y R rtodes Y R1 1 l m Which of the following best describes the relationship between 1 and 2? lternate interior angles onsecutive interior angles orresponding angles lternate exterior angles ommonwealth of Virginia epartment of Education 3

4 SESSION: 23 PE: 4 5/4/04 15:40 OIN IS-glenn Y ine l intersects lines w, x, y, and z, forming angles with measures as indicated on the drawing. l 7 In the figure drawn below, M and QR are parallel and m M m 60. Y rtodes 110 w Y R1 65 x rtodes Y R Which two lines are parallel? y z What is m QNP? w and x x and z y and z w and y 8 6 (4x 30) x 72 z l Y rtodes Y R1 Y (2x) y w m rtodes Y R1 Which value for x will make a parallel to b? Which additional piece of information would verify l m? x 72 y w z 108 x w 2004 ommonwealth of Virginia epartment of Education 4

5 SESSION: 23 PE: 5 5/4/04 15:40 OIN IS-glenn 9 R 11 Y rtodes Y R1 Which point lies on the line perpendicular to that bisects? Q R S T Q S T The drawing shows the arcs used to construct a bisector of a given angle an angle congruent to a given angle a bisector of a given line a perpendicular of a given line at a point on the line Y rtodes Y R1 10 Y rtodes Y R1 P Q R Which point lies on the bisector of PQR? 2004 ommonwealth of Virginia epartment of Education 5

6 SESSION: 23 PE: 6 5/4/04 15:40 OIN IS-glenn 12 onsider the following arguments. If the first two statements are true, in Y01602 which argument is the 3rd statement an incorrect conclusion? 1 If ohn studies, then he will pass the test. 2 If ohn passes the test, then he will not be grounded. 3 If ohn is grounded, then he will study. 1 If it rains, then we will stay inside. 2 Ifwestay inside, then we will play games. 3 Ifitrains, then we will play games. 13 ased strictly on this diagram, which is a valid conclusion? fish owners Pet Owners cat owners dog owners No cat owners also own dogs. No dog owners also own fish. No fish owners also own cats. No pet owner owns more than one pet. 14 onsider the following statements. Y01506 rtodes Y01506.R1 1 Ifwewin the game, then we will win the championship. 2 If we win the championship, then we will get a trophy. 3 Ifwedonot get a trophy, then we did not win the game. p: The sum of two angles is 90. q: The two angles are complements. Which of the following is a symbolic representation of the statement: If two angles are not complements, then the sum of the two angles is not 90? Y If Susan eats her broccoli, then she will get ice cream. 2 If Susan gets ice cream, then she will stay up late. 3 If Susan eats her broccoli, then she will stay up late. q p p q q p p q 2004 ommonwealth of Virginia epartment of Education 6

7 SESSION: 23 PE: 7 5/4/04 15:40 OIN IS-glenn 15 iven: and E 16 iven: R U. Y05405 T S Y05519 rtodes Y05405.R1 E X rtodes Y05519.R1 R U Which could be used to prove E? (SSS) If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent. (SS) If 2 sides and the angle between them in one triangle are congruent to 2 sides and the angle between them of another triangle, then the triangles are congruent. Which proportion is true? RT US TX SX RX UX RT XS RT US SX TX XT RX RT UX (S) If 2 angles and the sides between them are congruent to 2 angles and the side between them of another triangle, then the triangles are congruent. (S) If 2 angles and a side not between them are congruent to 2 angles and the side not between them of another triangle, then the triangles are congruent. 17 M N Q P Y05407 rtodes Y05407.R1 iven: MQ NP. Therefore M MN PQ Q N M NP MQ M P MN QP N P Q M 2004 ommonwealth of Virginia epartment of Education 7

8 SESSION: 23 PE: 8 5/4/04 15:40 OIN IS-glenn 18 P 20 Y mm 64 mm 650 m Y m rtodes Y R1 Q 70 mm R rtodes Y R1 rom smallest to largest, the angles of PQR are R, Q, P R, P, Q Q, R, P P, R, Q 19 Which set of lengths could not be the lengths of the sides of a triangle? Y in., 24 in., 30 in. 8 ft, 10 ft, 12 ft 4cm,5cm,9cm 2m,3m,4m The locations of three water pumping stations form a triangle on a map of the area. The distance from station to station is 650 meters. The distance from station to station is 558 meters. The distance from station to station is less than 92 m exactly 92 m between 92 m and 1,208 m greater than 1,208 m 21 The top of a ladder is leaning on a building at a point 12 feet above the ground; the bottom of the ladder is 5 feet from the base of the building. What is the length of the ladder? 19 ft 17 ft 13 ft 7ft Y ommonwealth of Virginia epartment of Education 8

9 SESSION: 23 PE: 9 5/4/04 15:40 OIN IS-glenn 22 Y rtodes 45 60? 23 6 in. 6 in. Y rtodes Y R1 Y R1 12 cm design is formed by joining isosceles right triangles and right triangles as shown in the diagram. If the hypotenuse of the triangle is 12 centimeters, which is closest to the length of one leg of the isosceles right triangle? 6cm 7.2 cm 8.5 cm 10.4 cm What is the diameter of the circle shown? 32 in. 33 in. 62 in. 63 in Y08506 Quadrilateral is a parallelogram. The measure of is rtodes Y08506.R ommonwealth of Virginia epartment of Education 9

10 SESSION: 23 PE: 10 5/4/04 15:40 OIN IS-glenn 25 The vertices of parallelogram have coordinates (1, 8), (4, 2), and (2, 7). Y08403 rtodes Y08403.R desktop was made from the scrap of plywood shown by cutting (in a straight line) from to E. Which measurement would ensure that the desktop is rectangular? E E E E E Y08615 rtodes Y08615.R1 What are the coordinates of? (5, 3) (3, 5) (2, 3) (5, 3) 27 Which of the following is not true about a parallelogram? ny two opposite sides are congruent. ny two opposite angles are congruent. The diagonals bisect each other. ny two consecutive angles are complementary. Y ommonwealth of Virginia epartment of Education 10

11 SESSION: 23 PE: 11 5/4/04 15:40 OIN IS-glenn 28 O O Y O O Y rtodes rtodes Y R1 What is the value of x in the pentagon above? What is the measure of interior angle of the regular polygon shown? Y R Y rtodes x 31 Y R1 P M Y Which is the closest to the measure of a central angle x in this regular polygon? If O is a diameter of circle P, what is m MO? O N rtodes Y R ommonwealth of Virginia epartment of Education 11

12 SESSION: 23 PE: 12 5/4/04 15:40 OIN IS-glenn 32 Secants P and P intersect the circle at and, respectively. 34 Y Y rtodes Y R1 5 4 Which could be the view of this stack of cubes from directly above? rtodes Y R1 P 12 What is the length of P? rtodes Y R2 Y R3 Y R4 Y R5 33 The figure shows a circle. m RPQ 50 and m PRQ 60. Y R 60 rtodes Y R1 P 50 Q What is the measure of PR? ommonwealth of Virginia epartment of Education 12

13 SESSION: 23 PE: 13 5/4/04 15:40 OIN IS-glenn 35 Y rtodes Y R1 36 tepee in the shape of a right cone has a slant height of 18.5 feet and a diameter of 20 feet. pproximately how much canvas would be needed to cover the tepee? 581 sq ft 116 sq ft 89 sq ft 58 sq ft Y rtodes Y R2 Y R3 Y R4 Y R5 Which piece completes this cube? 37 The reat Pyramid at iza has a square base with sides of length 230 meters and a height of meters. pproximately what is the volume of the reat Pyramid? 1,650,000 m 3 2,590,000 m 3 4,950,000 m 3 7,760,000 m 3 Y The ratio of the circumference of two circles is 3. The radius of the smaller 2 circle is 8 inches. What is the radius of the larger circle? inches 6 inches Y14R13 9 inches 12 inches 2004 ommonwealth of Virginia epartment of Education 13

14 SESSION: 23 PE: 14 5/4/04 15:40 OIN IS-glenn 39 Two ships leaving the same marina at the same time are 3.2 miles apart after Y14R54 sailing 2.5 hours. If they continue at the same rate and direction, how far apart will they be 2 hours later? 2.56 mi 3.52 mi 5.76 mi 6.08 mi 41 y ' ' ' x Y02407 rtodes Y02407.R1 40 XYZ was obtained from by a rotation about the point P. Y02513 rtodes Y02513.R1 P Z X Which of the following indicates the correspondence of the vertices? Y Triangle is apparently a translation of triangle across the x-axis a90 clockwise rotation of triangle about the origin a reflection of triangle across the y-axis a reflection of triangle across the x-axis X, Y, Z Y, Z, X X, Z, Y Z, X, Y 2004 ommonwealth of Virginia epartment of Education 14

15 SESSION: 23 PE: 15 5/4/04 15:40 OIN IS-glenn 42 y 43 y 5 Y Y02103 rtodes Y02730.R x x rtodes Y02103.R What is most likely the slope of the line graphed above? This figure is apparently symmetric with respect to the x-axis only the y-axis only both the x-axis and the y-axis neither the x-axis nor the y-axis ommonwealth of Virginia epartment of Education 15

16 SESSION: 23 PE: 16 5/4/04 15:40 OIN IS-glenn 44 y 45 The distance between the points Y02502 rtodes Y02502.R O x (2, 4) and (3, 8) is Y What are the apparent coordinates of the midpoint of diagonal? 1 2 1, 1 2,1 1, 1 2 (1, 1) 2004 ommonwealth of Virginia epartment of Education 16

17 SESSION: 26 PE: 17 5/24/04 13:0 OIN IS-glenn Test Sequence Number orrect nswer Reporting ategory nswer Key Reporting ategory escription ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles ines and ngles Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Triangles and ogic Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Polygons and ircles Three-imensional igures Three-imensional igures Three-imensional igures Three-imensional igures Three-imensional igures Three-imensional igures oordinate Relations and Transformations oordinate Relations and Transformations oordinate Relations and Transformations oordinate Relations and Transformations oordinate Relations and Transformations oordinate Relations and Transformations