# END OF COURSE GEOMETRY

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1 VIRGINI STNDRDS OF LERNING Spring 2010 Released Test END OF OURSE GEOMETRY Form M0110, ORE 1 Property of the Virginia Department of Education opyright 2010 by the ommonwealth of Virginia, Department of Education, P.O. ox 2120, 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 reproduce any portion of these released tests for non-commercial educational purposes without requesting permission. ll others should direct their written requests to the Virginia Department of Education, Division of Student ssessment and School Improvement, at the above address or by to

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3 Geometry Formula Sheet Geometric Formulas b 1 h h h h l b 1 2 = bh b 2 1 = 2 h(b 1 + b 2 ) V= h L.. = hp S..= L V= 3 h L..= 1 2 lp S..= L.. + w r r h r l =lw p= 2(l + w) b 4 3 h h l a c b =bh l w V = lwh S..= 2lw + 2lh + 2wh h 1 3 r b c 2 =a 2 + b 2 Example m D D Meaning angle measure of angle line segment measure of line segment line triangle rectangle D parallelogram D Geometric Symbols Example D D Meaning vector right angle Line is parallel to line D. Line is perpendicular to line D. ngle is congruent to angle. Triangle is similar to triangle. Similarly marked segments are congruent. Similarly marked angles are congruent. bbreviations Volume Lateral rea Total Surface rea rea of ase Pi 22 7 V L.. S.. opyright 2006 by the ommonwealth of Virginia Department of Education

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5 Geometry Directions Read each question and choose the best answer. SMPLE D E If is similar to DE,then : D =?: E. Which replaces the? to make the statement true? D E DE 3

6 1 bisector of contains which line segment? E D F G D G DF DG EF 4

7 2 Lines m and r are cut by a transversal. (3x 35) m (7x 115) r What value of x will show that line m is parallel to line r? F 20 G 24 H 25 J 33 3 a b 120º xº c 115º d If lines a and b are parallel, what is the value of x? D 60 5

8 4 Which point lies on the bisector of angle PQR? W X Y Z P Q R F G H J W X Y Z 5 For what measure of D is D in this figure? 85 E 26 D D 95 6

9 6 E D R P Q S T Which line segment is congruent to? F G H J PQ PR PS PT 7

10 7 In the figure shown, line q is a transversal of parallel lines l, m, n, and p. q x 30 y l m n p What are the values of x and y? x = 30, y= 30 x = 30, y= 150 x = 150, y= 30 D x = 150, y= 150 8

11 8 In the figure shown, parallel lines j and k are cut by transversal m. j k m 32 1 What is m 1? F 32 G 58 H 122 J 148 9

12 9 Lines y and z are cut by a transversal. 77 y x z For what value of x is y z? D

13 10 In this figure, m 1= ( 15x 5) and m 2= ( 10x+ 35). 1 2 What is m 1? F 31 G 65 H 85 J This figure represents line segments painted on a parking lot to create parking spaces. x w 118 Which equation can be used to show that these line segments are parallel? 118 w= x 118 x = w x = 180 D w =

14 12 Given: LMN 5 x + 5 L x x + 3 M 3x + 1 N What is the length of? F 11 G 12 H 22 J Given the following measures of the sides of triangles, which is a right triangle? D 41 cm, 40 cm, 9 cm 45 ft, 40 ft, 35 ft 52 in., 50 in., 11 in. 45 yd, 35 yd, 25 yd 12

15 14 Quadrilaterals Rectangles Rhombi Which of the following statements must be true about this Venn diagram? F G H J ll rectangles are rhombi. Some rhombi are rectangles. Quadrilaterals are not rhombi or rectangles. ll quadrilaterals are rhombi and rectangles. 13

16 15 Given: In this figure, and D bisect each other. E D ased on the information given, which triangle congruence theorem could be used to prove ED E? D ngle-ngle-side (S) ngle-side-ngle (S) Side-ngle-Side (SS) Side-Side-Side (SSS) 16 Statement: If lines are skew, then they are not coplanar. What is the contrapositive of the statement? F G H J If lines are not coplanar, then they are skew. If lines are not skew, then they are coplanar. If lines are coplanar, then they are not skew. If lines are skew, then they are coplanar. 14

17 17 oordinates ( 25, ), ( 6, 4),and ( 6, 0) are connected to form. y O x If D is congruent to, what are the coordinates of D? (, 11) (, 12) ( 2, 2) D ( 21, ) 15

18 18 Let p = n equation is of the form Let q = Its graph is a line. y= mx+ b. rgument: If an equation is of the form y= mx+ b, then its graph is a line. The graph is not a line. Therefore, the equation is not of the form y= mx+ b. Which of the following is the symbolic representation of the given argument? F p q q p G p q q p H p q p q J p q p q 16

19 19 TRG is a right triangle. R T G Which is closest to the length of RT? D 28 17

20 Which list has the sides of ordered from longest to shortest? F G H,,,,,, J,, 21 Three survey markers are located on a map at points H, I, and J. triangle is formed by connecting these markers by string so that HI = 150 feet, HJ = 245 feet, and IJ = 365 feet. Which statement is true about the measures of the angles of HIJ? D m H m H m I m I is the smallest is the largest is the smallest is the largest 18

21 22 6 x 45 In the figure, what is the value of x? F 6 G H J Two sides of a triangle measure 14 inches and 8 inches. Which cannot be the length of the remaining side? D 6 in. 8 in. 14 in. 21 in. 19

22 In the circle, what is the measure of? F 30 G 60 H 120 J This figure shows a pattern of triangles and regular hexagons. x What is the value of x? D

23 26 Which figure has all sides of equal measure but not necessarily all angles of equal measure? F G H J Square Rectangle Rhombus Trapezoid 27 What is m DRin circle? R 34 D D 68 21

24 28 Two chords intersect with the measures shown in the drawing x 12 What is the value of x? F 8.0 G 9.5 H 10.0 J In rectangle D, the slope of is. What is the slope of D? D 2 22

25 30 In the figure shown, what is m WXY? Y Z X W F 45 G 107 H 120 J DEFG is a rhombus with m EFG =28. D E G F What is m GDE? 14º 28º 30º D 56º 23

26 32 This figure is a traffic sign in the shape of a regular octagon. STOP x What is the value of x? F 45 G 60 H 135 J rectangular rug is 24 feet long and 10 feet wide. rhombus design is formed inside the rug by joining the midpoints of each side of the rectangle. What is the length of each side of the rhombus? D 13 ft 26 ft 169 ft 240 ft 24

27 34 man who is 6 feet tall casts a shadow that is 4 feet long. t the same time, a nearby flagpole casts a shadow that is 18 feet long. How tall is the flagpole? F G H J 10 ft 12 ft 22 ft 27 ft 35 fish tank in the shape of a rectangular prism has these dimensions: length = 20 inches width = 10 inches height = 12 inches What is the volume of water in the tank when it is D 1,120 cu in. 1,920 cu in. 2,400 cu in. 3,000 cu in. 4 5 full? 25

28 36 Which of these nets would form a cube when folded? F G H J 37 If a cube with side length 6 inches has its dimensions divided in half, what will be the volume of the new cube? D 108 cubic inches 54 cubic inches 27 cubic inches 9 cubic inches 26

29 38 right cone is placed on its circular base. ottom Which statement about the cone is incorrect? F G H J The view from the front is a triangle. The view from the bottom is a circle. The view from the top is a circle. The view from the left is a rhombus. 39 cone has a slant height of 10 centimeters and a lateral area of 60π square centimeters. What is the volume of a sphere with a radius equal to that of the cone? 102π cm 3 144π cm 3 288π cm 3 D 1, 333π cm 3 27

30 40 Which line of reflection maps point K at ( 2, 2 ) to point K at ( 2, 2)? F G H J y = 2 y= x x-axis y-axis 41 If the coordinates of are ( 1, 1) and the midpoint of is (, ), then the coordinates of 2 0 are ( 05., 05. ) ( 05., 05. ) ( 1, 0) D ( 5, 1) 28

31 42 Which transformation could move the triangle P to triangle P in a single step? y O P P' x F G H J Reflection over Rotation about Reflection over Translation x = 4 ( 23, ) y = 4 29

32 43 Figure STRFIND is symmetric with respect to the x-axis. The coordinates of point are ( 8, 6). What are the coordinates of point N? y S T D R I F x N ( 8, 6) ( 6, 8) ( 6, 8) D ( 8, 6) 30

33 44 Parallelogram RSTV has coordinates R( 0, 0), S( 2, 4), T( 6, 0), and V( 4, 4). Which ordered pair represents the intersection of the diagonals of this parallelogram? (The coordinate grid may be used to help answer this question.) y O x F G H ( 2, 0) ( 3, 0) ( 31, ) J ( 4, 1) 31

34 45 regular quadrilateral has what type of symmetry? D Line symmetry only Point symmetry only oth point and line symmetry Neither point nor line symmetry 32

35 nswer Key-EO021-M0110 Test Sequence Number orrect nswer Reporting ategory Reporting ategory Description 1 D 001 Lines and ngles 2 F 001 Lines and ngles 3 D 001 Lines and ngles 4 H 001 Lines and ngles Lines and ngles 6 G 001 Lines and ngles Lines and ngles 8 F 001 Lines and ngles Lines and ngles 10 J 001 Lines and ngles 11 D 001 Lines and ngles 12 G 002 Triangles and Logic Triangles and Logic 14 G 002 Triangles and Logic Triangles and Logic 16 H 002 Triangles and Logic 17 D 002 Triangles and Logic 18 F 002 Triangles and Logic Triangles and Logic 20 J 002 Triangles and Logic Triangles and Logic 22 G 002 Triangles and Logic Triangles and Logic 24 F 003 Polygons and ircles Polygons and ircles 26 H 003 Polygons and ircles 27 D 003 Polygons and ircles 28 F 003 Polygons and ircles Polygons and ircles 30 J 003 Polygons and ircles Polygons and ircles 32 F 003 Polygons and ircles Polygons and ircles 34 J 004 Three-Dimensional Figures Three-Dimensional Figures 36 F 004 Three-Dimensional Figures Three-Dimensional Figures 38 J 004 Three-Dimensional Figures Three-Dimensional Figures 40 G 005 oordinate Relations and Transformations 41 D 005 oordinate Relations and Transformations 42 J 005 oordinate Relations and Transformations oordinate Relations and Transformations 44 G 005 oordinate Relations and Transformations oordinate Relations and Transformations

36 Geometry, ore 1 If you get this many items correct: Then your converted scale score is:

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