END OF COURSE GEOMETRY

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1 SESSION: 35 PE: 3/0/06 :7 OIN IS-joer VIRINI STNRS O ERNIN Spring 005 Released Test EN O OURSE EOMETRY ORE Property of the Virginia epartment of Education 006 by the ommonwealth of Virginia, epartment of Education, P.O. ox 0, 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 retrieval system, without written permission from the copyright owner. ommonwealth of Virginia public school educators may reproduce any portion of these released tests for noncommercial educational purposes without requesting permission. ll others should direct their written requests to the Virginia epartment of Education, ivision of ssessment and Reporting at the above address or by to

2 006_eoormulaSht //05 0:07 M Page eometry ormula Sheet eometric ormulas b h h h h l b = bh b = h(b + b ) V = h.. = hp S..=.. + V = 3 h..= lp S..=.. + w r r h r l = lw p = (l + w) b 4 3 h h l a c b = bh l w V = lwh S..= lw + lh + wh h 3 r b c = a + b Example m Meaning angle measure of angle line segment measure of line segment line triangle rectangle parallelogram eometric Symbols Example Meaning vector right angle ine is parallel to line. ine is perpendicular to line. ngle is congruent to angle. Triangle is similar to triangle. Similarly marked segments are congruent. Similarly marked angles are congruent. bbreviations Volume ateral rea Total Surface rea rea of ase Pi 7 V.. S.. opyright 006 by the ommonwealth of Virginia epartment of Education

3 006_eoormulaSht //05 0:07 M Page

4 SESSION: 34 PE: /3/06 6:45 OIN IS-garyo eometry IRETIONS Read and solve each question. Then mark the space on the answer sheet for the best answer. SMPE E The figure shows line l intersecting lines r and s. l r s Y0306 rtodes Y0306.R In the figure, and are If is similar to E, then :?:E. Which replaces the? to make the statement true? E E alternate interior angles alternate exterior angles corresponding angles consecutive interior angles Y03050 The measures of some angles are given in the figure x rtodes Y03050.R 85 What is the value of x? ommonwealth of Virginia epartment of Education

5 SESSION: 34 PE: 3 /3/06 6:45 OIN IS-garyo 0587 Y rtodes Y R 3 The epartment of Transportation wants to extend the intersecting road across the highway, as indicated by the dotted line. x 55 intersecting road highway 4 The polygon shown is convex. E Y03063 rtodes Y03063.R new construction What should x be to ensure that the intersecting road and the new construction form a straight line? The sum of its interior angle measures is 900,60,60, l Y04077 m rtodes Y04077.R Which statement would be sufficient to prove that line l is parallel to line m? m l l 006 ommonwealth of Virginia epartment of Education 3

6 SESSION: 34 PE: 4 /3/06 6:45 OIN IS-garyo Y rtodes Y R 6 In this diagram, line d cuts three lines to form the angles shown d 7 Quadrilateral QRST is placed on a coordinate grid as shown. y T (4, 6) S (?,?) Y0404 rtodes Y0404.R a b c Which two lines are parallel? a and b a and c b and c No lines are parallel. Q (0, 0) R (8, 0) What coordinates for S make QRST a parallelogram? x (8, 6) (8, 0) (, 6) (, 0) 8! " $ # % & l m Y04073 rtodes Y04073.R Which condition will guarantee that line l is parallel to line m? ommonwealth of Virginia epartment of Education 4

7 SESSION: 34 PE: 5 /3/06 6:45 OIN IS-garyo Y0305 rtodes Y0305.R The drawing shows a compass and straightedge construction of a perpendicular to a given line from a point not on the line a perpendicular to a given line at a point on the line the bisector of a given angle an angle congruent to a given angle To which point should a line segment from be drawn so that the resulting figure is a rectangle? W X Y Z W X Y Z Y05 rtodes Y05.R 0 Y 0557 Y0606 rtodes Y0606.R W X Z XYZ is similar to STR. XY 6 and ST. If the perimeter of STR is 38, then what is the perimeter of XYZ? Y0563 l T Which point would be on a line perpendicular to l through T? W X Y Z 006 ommonwealth of Virginia epartment of Education 5

8 SESSION: 34 PE: 6 /3/06 6:45 OIN IS-garyo et p represent Y0804 z, and let q represent z is a rational number. Which is a representation of the statement below? 5 Which of the following statements represents a valid argument? If a b and a c, then b c. If a b and b c, then a c. If a b and a c, then c b. If a b and a c, then a b c Y0407 If z, then z is not a rational number. p q p q p q q p 6 iven: XY YX Y0550 rtodes Y0550.R X Y Isosceles Triangles Y050 Equilateral Triangles rtodes Y050.R Which is a true proportion? ccording to the Venn diagram, which statement is true? X Y XY ll isosceles triangles are also equilateral triangles. X X Y Y XY ll equilateral triangles are also isosceles triangles. Some equilateral triangles are also isosceles triangles. No isosceles triangles are equilateral triangles. X X Y Y XY X Y XY 006 ommonwealth of Virginia epartment of Education 6

9 SESSION: 34 PE: 7 /3/06 6:45 OIN IS-garyo iven: and intersect at X X X X X Y05508 rtodes Y05508.R Which congruency statement is true? X X X X X X X X X 9 In the drawing of triangle XYZ, which angle has the least measure? Y 5 ll angles have the same measure. XYZ ZXY XZY X 6 7 Z Y rtodes Y R Which list could not be the measures of lengths of the three sides of a given triangle? Y cm, cm, 5 cm ft,6ft,5ft mi, 4 mi, mi yd, 35 yd, 0 yd 0 If m 65, m 5, m 00, which lists the sides of the triangle in order from shortest to longest?,,,,,,,, Y ommonwealth of Virginia epartment of Education 7

10 SESSION: 34 PE: 8 /3/06 6:45 OIN IS-garyo 0547 windlass is used to pull a boat to the dock. The rope is attached to the boat at a point 7 feet below the level of the windlass. Y X Y 45 5 Z 0555 Y rtodes Y R rtodes Y07058.R 7 ft 5 ft or the triangle represented by the above drawing, what is the length of XZ? x ft What is the distance from the boat to the dock when the rope is 5 feet? ft 4 ft 8 ft 7ft 4 E 8400 Y The parallelogram has the measurements shown. Y rtodes Y R 0 63 h 5 In rectangle, which of the following pairs of segments are not necessarily congruent? and and and E and E rtodes Y08709.R Which is closest to the length of the altitude, h? ommonwealth of Virginia epartment of Education 8

11 SESSION: 34 PE: 9 /3/06 6:45 OIN IS-garyo The town plaza in a certain town is a parallelogram. The town s planning committee has decided to build a fountain at the center of the plaza. This sketch shows the corner points when placed on a coordinate grid. Y Quadrilateral is a parallelogram. 057 Y0860 rtodes Y0860.R rtodes Y0856.R (0, 4) Which of the following must be true? (, 0) (6, ) (4, 3) Which coordinates show where the fountain will be located? (, 0.5) (0.5, ) (3,.5) (.5, ) 7 is a rhombus Y0807 rtodes Y0807.R What is the measure of? ommonwealth of Virginia epartment of Education 9

12 SESSION: 34 PE: 0 /3/06 6:45 OIN IS-garyo If each interior angle of a regular polygon measures 0, how many sides does the polygon have? Y TV is a diameter of circle Z. T S 8 x U Z Y0070 rtodes Y0070.R Which angle measure below is not a possible measure of an exterior angle of a regular polygon? Y V What is the value of x? Y09067 rtodes Y09067.R 70 In the figure, what is the measure of? 3 O If P 8 and P 4, what is the measure of, the diameter of this circle? P Y000 rtodes Y000.R ommonwealth of Virginia epartment of Education 0

13 SESSION: 34 PE: /3/06 6:45 OIN IS-garyo TW is a diameter of circle X, and TW is parallel to UV. Y0060 T 5 U 34 This is a scale drawing of a tent where centimeter represents 0.5 meter. cm 0.5 m Y030 rtodes Y0060.R rtodes Y030.R X W V If the measure of TU is 5, what is the degree measure of UV? What is the height of the tent at its highest point? 0 m 5m 3m.5 m 006 ommonwealth of Virginia epartment of Education

14 SESSION: 34 PE: /3/06 6:45 OIN IS-garyo Y00 rtodes Y00.R Which represents a two-dimensional view from directly above the figure? 37 spherical paintball measures.5 centimeters in diameter. pproximately how much paint is in it?.77 cm cm cm cm Y rtodes Y00.R Y00.R3 Y00.R4 Y00.R Which proportion can be used to find the value of PR if XMQ is similar to PRS? PR 0573 Y4R6 rtodes Y4R6.R To the nearest gallon, what is the volume of a cylindrical water heater.4 feet in diameter and 4 feet tall? ( cubic foot 7.48 gallons) Y gal 46 gal 59 gal 3 gal PR PR PR 006 ommonwealth of Virginia epartment of Education

15 SESSION: 34 PE: 3 /3/06 6:45 OIN IS-garyo When standing upright, ary knows his eyes are 6 feet above ground level. To determine the depth of a well, he stands in the position shown. Y4R40 40 ( 7, ) (3, 8) Y00 rtodes Y00.R 6 ft O rtodes Y4R40.R ft 6 ft The coordinates of the midpoint of are (5, 3) (5, 3) (, 5) (, 5) Using the given measures, how deep is the well? ft 4 ft 6 ft 8 ft 006 ommonwealth of Virginia epartment of Education 3

16 SESSION: 34 PE: 4 /3/06 6:45 OIN IS-garyo Parallelogram is placed on a coordinate grid as shown. Y07 5 y 4 y ' ' 0579 Y04 rtodes Y07.R 4 3 ' x rtodes Y04.R O x Triangle is What is the approximate length of diagonal? 3.0 units 5.4 units 9.0 units 0.6 units a translation of triangle across the y-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 006 ommonwealth of Virginia epartment of Education 4

17 SESSION: 34 PE: 5 /3/06 6:45 OIN IS-garyo ow many different lines of symmetry does a square have? Y y x Y060 rtodes Y060.R Which is most likely the slope of the line graphed? ommonwealth of Virginia epartment of Education 5

18 SESSION: 34 PE: 6 /3/06 6:45 OIN IS-garyo 45 l Y050 rtodes Y050.R P m E exagon E is apparently symmetric with respect to point P only line m only line l only both lines l and m only 006 ommonwealth of Virginia epartment of Education 6

19 SESSION: 34 PE: 7 /3/06 6:45 OIN IS-garyo Test Sequence Number orrect nswer Reporting ategory nswer Key Reporting ategory escription 00 ines and ngles 00 ines and ngles 3 00 ines and ngles 4 00 ines and ngles 5 00 ines and ngles 6 00 ines and ngles 7 00 ines and ngles 8 00 ines and ngles 9 00 ines and ngles 0 00 ines and ngles 00 ines and ngles 00 Triangles and ogic 3 00 Triangles and ogic 4 00 Triangles and ogic 5 00 Triangles and ogic 6 00 Triangles and ogic 7 00 Triangles and ogic 8 00 Triangles and ogic 9 00 Triangles and ogic 0 00 Triangles and ogic 00 Triangles and ogic 00 Triangles and ogic 3 00 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

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