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VIRGINIA STANDARDS OF LEARNING Spring 2007 Released Test END OF COURSE GEOMETRY Form M0117, CORE 1 Property of the Virginia Department of Education ©2007 by the Commonwealth of Virginia, Department of Education, P.O. Box 2120, Richmond, Virginia 23218-2120. All 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. Commonwealth of Virginia public school educators may reproduce any portion of these released tests for non-commercial educational purposes without requesting permission. All others should direct their written requests to the Virginia Department of Education, Division of Student Assessment and School Improvement, at the above address or by e-mail to [email protected]. ISD6736 Geometry Formula Sheet Geometric Formulas b1 h h b A= 1 2 h h B b2 bh A= 1 2 l V = Bh L.A. = hp S.A.= L.A. + 2B h(b1 + b2 ) V = 13 Bh L.A.= 12 lp S.A.= L.A. + B r w r r h l 4 3 A = lw p = 2(l + w) b h l h h b A = bh l w V = lwh S.A.= 2lw + 2lh + 2wh m A Meaning angle A Example AB measure of angle A 1 3 line segment AB AB CD AB measure of line segment AB AB CD AB line AB A ABC triangle ABC A ABCD rectangle ABCD ABCD parallelogram ABCD Copyright © 2006 by the Commonwealth of Virginia Department of Education c2 = a2 + b2 Abbreviations Meaning vector AB right angle AB b r Geometric Symbols Example A c a Line AB is parallel to line CD. Line AB is perpendicular to line CD. B Angle A is congruent to angle B. B Triangle A is similar to triangle B. Similarly marked segments are congruent. Similarly marked angles are congruent. V L.A. S.A. Volume Lateral Area Total Surface Area Area of Base B Pi 22 7 Geometry Directions Read each question carefully and choose the best answer. Then mark the space on your answer document for the answer you have chosen. SAMPLE A D E B C If ABC is similar to ADE , then AB : AD = ? : AE. Which replaces the “?” to make the statement true? A B C D AC AE DE BC 5 1 Transversal l cuts lines a, b, c, and d. l 75° a 85° b c 105° 100° d Which two lines are parallel? A B C D a a b b and and and and c d c d 6 2 1 2 3 4 5 6 7 8 In the figure above, ∠2 and ∠6 are a pair of — F G H J 3 consecutive interior angles alternate interior angles vertical angles corresponding angles One exterior angle of a regular polygon measures 72°. What is the measure of one interior angle? A 18° B 108° C 360° D 540° 7 4 In this drawing, a b and c d . b a 1 2 5 6 9 10 13 14 3 4 7 8 11 12 c d 15 16 Which angle is not necessarily congruent to ∠1? F ∠3 G ∠9 H ∠12 J ∠16 8 5 The support legs on a bench are attached in such a way that the angle made by one leg with the ground is 130°. x 130° What must the measure of the angle marked x be in order for the seat of the bench to be parallel to the ground? A 50° B 65° C 90° D 130° 9 6 Line v is a transversal. v 70° w x y 80° 110° z 100° Which is a true statement? F w y and x z G w x and y z H w z and x y J w x and x y 10 7 1 5 2 3 4 6 7 8 9 10 11 12 13 14 15 16 o l m n In the drawing above, ∠ 4 and ∠12 are — A B C D 8 alternate interior angles consecutive interior angles corresponding angles a linear pair A carpenter nailed a board across two beams, forming the angles shown. 6 2 5 1 3 4 Which equal measures would ensure the beams are parallel? F G H J m ∠1 = m ∠ 2 m ∠1 = m ∠ 3 m∠2 = m∠5 m∠3 = m∠ 4 11 9 C A B K L N M R Which segment is congruent to AB ? A CK B CL C CM D CN 12 10 W Y Z X l A Which point apparently lies on the perpendicular to l from A? F G H J X Y Z W 13 11 One piece of pie is left for two boys to share. X W Y Z C Where should the pie be cut to ensure each gets an equal piece? A CZ B CY C CX D CW 14 12 13 If p → q , and q → r , then — F r →p G p →r H ∼r → p J r →∼p If the conditional statement “If you have a laptop, then you have a computer” is represented by p → q , what is the symbolic representation of “If you have a computer, then you do not have a laptop”? A B C D q →∼p ∼q →p p →∼q ∼q →∼p 15 14 In the Venn diagram below, V represents the set of all vehicles, M represents the set of all motorized vehicles, and A represents the set of all automobiles. V M A Based on the diagram, which is a valid conclusion? F G H J All automobiles are motorized vehicles. All motorized vehicles are automobiles. Some automobiles are not motorized vehicles. No automobiles are motorized vehicles. 16 15 Which triangle below is not congruent to the other three triangles? 70° A 9 B 9 70° C 9 D 9 17 16 N K 12 L 8 M I 12 10 J Which additional piece of information would prove that IJK ∼LMN ? F NM = 18 G LM = 18 H NM = 15 J LM = 10 18 17 Given: M is the midpoint of LN and KP . K N M J O L P The given information is sufficient to prove postulate/theorem? A B C D 18 KML ≅ PMN by which Angle-Side-Angle Side-Side-Side Side-Angle-Side Angle-Angle-Side Which of the following could not be the lengths of the sides of a triangle? F G H J 6 3 4 5 ft, 3 ft, 9 ft cm, 4 cm, 5 cm in., 6 in., 8 in. km, 2 km, 4 km 19 19 20 In DEF , mDE = 8 inches , mEF = 6 inches , and mDF = 10 inches. Which lists the angles in order from smallest to largest ? A ∠D , ∠E , ∠F B ∠F , ∠D , ∠E C ∠E , ∠F , ∠D D ∠D , ∠F , ∠E In ABC , if m∠C < m∠B < m∠A , then — F AB < AC < BC G AC < AB < BC H AB < BC < CA J BC < AB < CA 20 21 To mark the end of a race, a finish-line banner is stretched across the road as shown in the drawing. Finish Line x 7 ft 8 ft Which is closest to the length of the support rope designated by x in the drawing? A B C D 9.5 ft 10.6 ft 12.0 ft 15.0 ft 21 22 A baseball diamond is in the shape of a square, 90 feet on a side. 2nd Base 90 ft 90 ft 3rd Base 1st Base 90 ft 90 ft Home What is the direct distance from home plate to second base? F 90 ft G 90 2 ft H 90 3 ft J 180 ft 22 23 What is the length of a diagonal brace that could be used for a wall 9 feet high and 12 feet long? A B C D 12 13 14 15 ft ft ft ft 23 24 Gene’s horse corral, labeled ABCD in the drawing, is shaped as a parallelogram and is adjacent to the shed, labeled ZAD. A Z B Shed Corral F 40° D C G If a gate, labeled CF, opens all the way to the corral fence, position labeled CG, through how many degrees does the gate swing? F G H J 25 40° 50° 130° 140° A diagonal of parallelogram DEFG forms angles with measures as shown. D E 56° 44° G F What is the measure of ∠DEF ? A B C D 44° 56° 80° 100° 24 26 y 9 8 7 6 5 M 4 3 2 N 1 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 –1 O 1 2 3 4 5 6 7 8 9 x –2 –3 –4 –5 –6 –7 –8 –9 Quadrilateral MNOP is a parallelogram. The coordinates of three of its vertices ( ) ( ) are M 1, 5 , N 2 ,1 , and O value of x ? F − 5 G − 4 H − 3 J 0 ( − ) ( ) 3, − 2 . If x , 2 are the coordinates of P, what is the 25 27 Rectangular flowerbeds are built on each side of a fishpond in the shape of a regular octagon. x What is the measure of the angle, x, between two consecutive flowerbeds? A 30° B 45° C 60° D 90° 28 24° A portion of a regular polygon is shown. The polygon has — F G H 15 sides 16 sides 18 sides J 20 sides 26 29 Each interior angle of a regular polygon has a measure of 162°. The polygon has a total of — A B C D 30 17 18 19 20 sides sides sides sides is 280º. In circle O, the degree measure of PSR P S R O What is the degree measure of ∠ POR ? F G H J 160° 85° 80° 40° 27 31 A B 26 20 2x + 6 D 40 What is the value of x in trapezoid ABCD ? A B C D 17 13 10 7 28 C 32 In circle C , m W X = 25°, m XY = 40°, m YZ = 25°, and WY = 24 centimeters. Y X W Z C What is the length of XZ ? F G H J 33 12 24 25 65 cm cm cm cm A pizza has a diameter of 16 inches. Which is closest to the area of one slice if the pizza is divided into 6 equal pieces? A B C D 134.1 sq in. 117.1 sq in. 67.2 sq in. 33.5 sq in. 29 34 Assuming the solid is constructed from cubes measuring 1 unit on each edge and that the figure is completely solid, what is the volume of the cubic solid shown above? F G H J 12 34 59 68 cubic cubic cubic cubic units units units units 30 35 Which could not be a two-dimensional view of the block of cubes shown above? A B C D 36 Which is closest to the volume of a sphere with a radius equal to 8 centimeters? F G H J 267.9 cm3 803.8 cm3 1,607.7 cm3 2,143.6 cm3 31 37 What is the total surface area of a rectangular prism box that measures 5 feet by 1 foot by 1 foot? A B C D 5 sq ft 20 sq ft 22 sq ft 30 sq ft 38 S P3 0m 28 m Blue Lake R Q 10 5m T If PQ is parallel to ST, what is ST, the width of the lake? F G H J 62 70 84 98 meters meters meters meters 32 39 The ratio of the perimeter of U to the perimeter of y x 2 V is 1 : 2. 4 V U z 5 If the triangles are similar, what is the value of x + y ? A B C D 3 6 12 18 33 40 Right triangle ABC has the measures shown. A 5 C 4 3 B What is the maximum number of different lines of symmetry that can be drawn through ABC ? F G H J 0 1 2 3 34 41 y Q 5 4 3 2 1 -5 -4 -3 -2 -1 O -1 -2 -3 -4 -5 1 2 3 4 5 V What is the apparent slope of QV ? A B C D −2 –1 2 1 2 2 35 x 42 y x 0 In relation to one figure, the other figure is apparently a — F reflection across the line y = 1 G reflection across the line y = x H 90° rotation about the origin J 180° rotation about the origin 36 43 Triangle ABC is placed on a grid as shown. y 9 8 7 A 6 5 4 B 3 2 1 -2 -1 C O 1 2 3 -1 The apparent midpoint of AB is — A B C D (1.5, 1.5) (3, 3) (4.5, 4.5) (4.5, 1.5) 37 4 5 6 7 x 44 Rectangle ABCD is placed in a coordinate plane as shown. y A D 9 8 7 6 5 4 3 2 1 -9 -8 -7- 6 - 5 -4 - 3 -2-1 O -1 -2 B C 1 2 3 4 x Which equation describes a line of symmetry for rectangle ABCD ? F G H J x x y y =2 =5 =5 =x 38 45 y=x y 5 B 4 3 A C 2 B' 1 – 5 – 4 – 3 – 2 – C' 1 0 – 1 – 2 – 3 – 4 – 5 1 A' A ′B ′C ′ is apparently the result of — A B C D 2 ABC across the y-axis reflecting ABC across the x-axis rotating ABC about the point (1, 2) reflecting ABC across the line y = x reflecting 39 3 4 5 x Answer Key-EOC021-M0117 Test Sequence Number Correct Answer 1 A 2 J 3 B 4 H 5 A 6 F 7 C 8 G 9 D 10 F 11 C 12 G 13 A 14 F 15 D 16 F 17 C 18 F 19 D 20 F 21 B 22 G 23 D 24 H 25 C 26 G 27 B 28 F 29 D 30 H 31 D 32 G 33 D 34 G 35 C 36 J 37 C 38 J 39 C Reporting Category 001 001 001 001 001 001 001 001 001 001 001 002 002 002 002 002 002 002 002 002 002 002 002 003 003 003 003 003 003 003 003 003 003 004 004 004 004 004 004 Reporting Category Description Lines and Angles Lines and Angles Lines and Angles Lines and Angles Lines and Angles Lines and Angles Lines and Angles Lines and Angles Lines and Angles Lines and Angles Lines and Angles Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Triangles and Logic Polygons and Circles Polygons and Circles Polygons and Circles Polygons and Circles Polygons and Circles Polygons and Circles Polygons and Circles Polygons and Circles Polygons and Circles Polygons and Circles Three-Dimensional Figures Three-Dimensional Figures Three-Dimensional Figures Three-Dimensional Figures Three-Dimensional Figures Three-Dimensional Figures 40 F 005 Coordinate Relations and Transformations 41 B 005 Coordinate Relations and Transformations 42 J 005 Coordinate Relations and Transformations 43 C 005 Coordinate Relations and Transformations 44 H 005 Coordinate Relations and Transformations 45 D 005 Coordinate Relations and Transformations Geometry, Core 1 If you get this many items correct: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Then your converted scale score is: 000 182 217 238 254 266 277 286 294 302 309 315 321 327 332 338 343 348 353 358 363 368 372 377 382 387 391 396 401 406 411 417 422 428 434 441 448 455 464 473 483 496 512 533 568 600