Georgia Standardized Test Practice Workbook

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GeorgiaStandardized TestPractice WorkbookMcDougal Littellcorrelated to theGEORGIA QUALITY CORE CURRICULUMand theGEORGIA HIGH SCHOOL GRADUATION TEST STANDARDS

GeometryApplying Reasoning MeasuringGeorgia GeometryStandardized TestPractice WorkbookThe Standardized Test Practice Workbook providespractice exercises for every lesson in a standardized testformat. Included are multiple-choice, quantitativecomparison, and multi-step problems. The StandardizedTest Practice for every lesson is correlated to the GeorgiaQuality Core Curriculum and to the Georgia High SchoolGraduation Test standards. At the end of the book youwill find practice for the Georgia End-of-Course Test.

Copyright 2001 McDougal Littell Inc.All rights reserved.Permission is hereby granted to teachers to reprint or photocopyin classroom quantities the pages or sheets in this work that carrya McDougal Littell copyright notice. These pages are designedto be reproduced by teachers for use in their classes withaccompanying McDougal Littell material, provided each copymade shows the copyright notice. Such copies may not be sold,and further distribution is expressly prohibited. Except asauthorized above, prior written permission must be obtained fromMcDougal Littell Inc. to reproduce or transmit this work or portionsthereof in any other form or by any other electronic or mechanicalmeans, including any information storage or retrieval system,unless expressly permitted by federal copyright law. Addressinquiries to Manager, Rights and Permissions, McDougal LittellInc., P. O. Box 1667, Evanston, Illinois 60204.ISBN: 0-618-13259-7123456789-MDI- 04 03 02 01 00

ContentsChapter Title1Basics of Geometry2Reasoning and Proof3Perpendicular and Parallel Lines14–204Congruent Triangles21–275Properties of Triangles28–336Quadrilaterals34–40Cumulative Standardized Test 1–579Right Triangles and Trigonometry58–6410Circles65–7111Area of Polygons and Circles72–7712Surface Area and Volume78–84Georgia End-of-Course Practice Test85–88AnswersCopyright McDougal Littell Inc.All rights reserved.1–78–13A1-A8GeometryGeorgia Standardized Test Practice Workbookiii

LESSON1.1GA QCC: 4, 6Standardized Test PracticeFor use with pages 3–9TEST TAKING STRATEGY1. Multiple ChoiceRead each test question carefully. Always look for shortcuts that will allow you to work through a problem morequickly.Choose the next figure inthe pattern.Choose the next figure inthe pattern.BDECWhat is the next number inthe sequence?ABDEChapter 1A2. Multiple Choice5. Multiple ChoiceC6. Multiple ChoiceThe first three objects in apattern are shown. How many blocks are inthe next object?2, 21, 24, 27 . . .A29B210D211E2123. Multiple ChoiceC10What is the next number inthe sequence?A20B25D36E40C300, 2, 6, 12 . . .A18B24D22E26C207. Multi-Step ProblemExamine the triangularpattern.14. Multiple Choice1What is the next number in1the sequence?22, 4, 16 . . .A28B26D256E192C2121211 3 3 1a. Predict the next two rows of the triangle.b. Describe a pattern for the value of a num-ber in each row.c. Describe a pattern for the number ofentries in each row.Copyright McDougal Littell Inc.All rights reserved.GeometryGeorgia Standardized Test Practice Workbook1

LESSONGA QCC: 7, 9, 121.2Standardized Test PracticeFor use with pages 10–16TEST TAKING STRATEGYWork as quickly as you can through the easier sections butavoid making careless errors on easy questions. What does the symbol BC1. Multiple Choice?represent?Chapter 1 AB and BD intersect at7. Multiple Choice.Asegment BCBline BCAABBCpoint BDray BCDDEnone of theseEray CBbaMPNYcOQRC8. Multiple ChoiceMultiple Choice In Exercises 2–6, refer tothe diagram below.XCPoints W, X, Y and Z arenot coplanar. What is the intersection of planeWXY and WYZ? AWXBWYC W and YDThe planes do not intersect.ECannot be determined.9. Multi-Step ProblemFollow the directionsbelow to sketch the desired shape.dZa. Draw a plane. Label the four corners A, B,2. Name a point that is collinear to points Nand Z.APBODP and XEO and MCMCZ3. Name a point that lies on line c.AMBPDQEOC, and D, starting at the bottom left andproceeding clockwise. b. Draw four parallel lines, AE, BF, CG, and DH, so that each line intersects planeABCD once, and points E, F, G, and H arecoplanar. Plane ABCD and plane EFGHare parallel.c. Draw EH, HG, FG, and EF.d. What shape is outlined by the figure?4. Name a point that is collinear to points Pand Q.AMBNDXEM and YCY5. Name a point that is coplanar to line a.ANBODQEall of theseCRCM, N, Z6. Name three noncollinear points.2AP, Y, QBM, N, PDQ, R, OEX, N, PGeometryGeorgia Standardized Test Practice WorkbookCopyright McDougal Littell Inc.All rights reserved.

LESSON1.3GA QCC: 7, 8, 9, 12, 43,46Standardized Test PracticeGHSGT: 9, 19, 20, 35For use with pages 17–25TEST TAKING STRATEGYSketch graphs or figures in your test booklet to help yousolve the problems. Even though you must keep youranswer sheet neat, you can make any kind of mark youwant in your test booklet.1. Multiple ChoiceA rule that is acceptedwithout proof is called a? .theoremBpostulateCaxiomDA and BEB and CFind the length of AC ifAB is 6, BC is 10, and B is between A and C.2. Multiple 5B10D20E25C15C15CANP 5 MN 1 PQ BMP 5 OQCNQ 5 MPMO 5 PQEMQ 5 PQ ? 3Copyright McDougal Littell Inc.All rights reserved.E39?In Exercise 8, the length.A3B5D31E39C7AAB BCBAB CDCAB BDDAC ABEBC CDAThe value in column A is greater.BThe value in column B is greater.CThe two values are equal.DThe relationship cannot be determinedfrom the information given.Column AColumn B11.AB when As1, 3d andBs3, 26dXY when Xs5, 2dand Ys21, 4d12.AB when As22, 24dand Bs3, 2dXY when Xs25, 3dand Ys28, 22d13.XZXY 1 YZ157. Which of the statements below are not true?D317In Exercises11–13, choose the statement below thatis true about the given values.6. Find the length of NP.ADCQuantitative Comparison5. Find the length of NO.A5Use points As5, 1d,Bs5, 6d, Cs1, 4d and Ds4, 22d to determinewhich of the following is true.154. Find the length of PQ.AB10. Multiple Choice3. Find the length of OQ.53of HI isQAA9. Multiple Choice24Multiple Choice In Exercises 3–7, use thediagram below where MQ 5 30, MN 5 5,MN 5 NO and OP 5 PQ.MPoint H is between G andI. Use the segment addition postulate to solvefor x when GH 5 8x 1 7, HI 5 3x 2 2, andGI 5 38.GeometryGeorgia Standardized Test Practice Workbook3Chapter 1A8. Multiple Choice

LESSON1.4GA QCC: 8, 9Standardized Test PracticeGHSGT: 29, 31For use with pages 26–32TEST TAKING STRATEGYAvoid spending too much time on one question. Skipquestions that are too difficult for you, and spend nomore than a few minutes on each question.A08 m/A 908Plot the points As26, 4d,Bs21, 1d and Cs3, 1d in a coordinate plane.Sketch /ABC. The angle is a(n)? .B08 m/A 1808Aacute angleBobtuse angleC908 m/A 1808Cright angleDstraight angleDm/A 5 908Eadjacent angleEm/A 5 1808Angle A is an obtuse anglefor which measure(s)?Chapter 11. Multiple Choice2. Multiple Choicewould be a(n)6. Multiple Choice7. Multiple ChoiceUsing the same three pointsin Exercise 6, sketch /ACB. The angle is a(n)? .An angle measuring 358? .Aacute angleBobtuse angleCright angleDstraight angleEadjacent angle3. Multiple ChoiceWhich angle appears to bea right angle?8.Aacute angleBobtuse angleCright angleDstraight angleEadjacent angleQuantitative ComparisonUse thefollowing information.ABCD D is interior to /ABE m/ABD 5 508 E is interior to /DBF m/EBC 5 908 F is interior to /EBC m/ABD 5 m/EBFChoose the statement below that is trueabout the given values.E4. Multiple ChoiceA58C858E1758Find m/WYZ.BD908W1058X458408Y5. Multiple ChoiceZFind the measure ofAThe value in column A is greater.BThe value in column B is greater.CThe two values are equal.DThe relationship cannot be determinedfrom the information given.Column AColumn Bm/ABCm/ABE 1 metryGeorgia Standardized Test Practice WorkbookCopyright McDougal Littell Inc.All rights reserved.

LESSON1.5GA QCC: 9, 15, 43, 46Standardized Test PracticeGHSGT: 4, 31For use with pages 34–42TEST TAKING STRATEGYStaying physically relaxed during the SAT is very important.If you find yourself tensing up, put your pencil down andtake a couple of deep breaths. This will help you stay calm.1. Multiple ChoiceFind the midpoint of a segment with endpoints As3, 22d and Bs8, 1d.ABEs112, 12 ds112, 2 32 dCs112, 2 12 d2. Multiple ChoiceFind the midpoint of a segment with endpoints As27, 3d and Bs3, 23d.s22, 23dBCs25, 0dDEs25, 23dAA148B288D628E15287. Multiple Choices22, 0ds2, 0dA268B528C1048D138ECs3, 7dEs229, 211dMS528388QFind the coordinates of theother endpoint of a segment with an endpointof Xs13, 5d and midpoint Ms8, 3d.s18, 7d QS bisects /MQR. Whatis the m/MQR?3. Multiple ChoiceA568C8. Multiple ChoiceR AB bisects /CAD. Findthe value of x.Bs18, 1dA2B56Ds3, 1dC5D28E6C(8x 2 20)8B( x 1 25)812AFind the coordinates of theother endpoint of a segment with an endpointof Xs22, 3d and midpoint Ms1, 22d.D4. Multiple ChoiceAs4, 27dBs24, 7dCs0, 21dDs25, 8dEs4, 8dQuantitative ComparisonIn Exercises 9 and 10, use the diagram below where BD bisects /ABC and BE bisects /ABD.Choose the statementbelow that is trueEAabout the given values.288D5. Multiple ChoiceAThe value in column A is greater.A/A and /BBB/A and /CThe value incolumn B is greater.C/B and /CCThe two values are equal.DAB and ACDThe relationship cannot be determined.EAB and BCChoose the congruentangles on the triangle shown.Copyright McDougal Littell Inc.All rights reserved.BACBCColumn AColumn B9.m/ABE 1 m/EBDm/DBC10.m/ABD1808GeometryGeorgia Standardized Test Practice Workbook5Chapter 1Ds52, 2 32 ds52, 2 12 d BD bisects /ABC. If them/DBC 5 288, what is the m/ABD?6. Multiple Choice

LESSONGA QCC: 8, 9, 121.6Standardized Test PracticeGHSGT: 29, 31For use with pages 44–50TEST TAKING STRATEGYThe mathematical portion of the SAT is based on materialtaught in your high school mathematics courses. One ofthe best ways to prepare for the SAT is to keep up withyour regular studies and do your homework assignments.Multiple Choice Refer to the diagrambelow for Exercises 1–3.6. Multiple ChoiceFind the value of x.(4x 2 5)8Chapter 1(3x 1 2)82 315A13.3B7D26E254C147. Multiple ChoiceA/1 and /2B/2 and /3Two angles are complementary. One angle has a measure that istwice the other angle. What is the measureof the smaller angle?C/1 and /4D/4 and /5A15B30E/3 and /5D60E751. Which angles are a linear pair?2. Which angles are vertical angles?8. Multiple ChoiceA/1 and /2B/1 and /5C/3 and /5D/1 and /4E/4 and /5/1 and /4B/4 and /5C/1 and /5DB and CEall of metryGeorgia Standardized Test Practice Workbook10B28D152E128AWhat is the m/1?5. Multiple ChoiceAC20In Exercises 9and 10, use the diagram below andchoose the statement below that is trueabout the given value. The m/3 5 768.Two angles are supplementary. One angle has a measure that is five lessthan four times the other. What is the measureof the larger angle?19Find the value of y.Quantitative Comparison4. Multiple ChoiceA45(4x 2 12)8(2x 1 8)8(7y 1 12)83. Which angles are supplementary?AC9.The value incolumn A is greater.213BThe value in columnB is greater.CThe two values areequal.DThe relationship cannot be determinedfrom the given information.Column A4Column Bm/3m/1m/4The supplement of /110.Copyright McDougal Littell Inc.All rights reserved.

LESSONGA QCC: 12, 37, 461.7Standardized Test PracticeGHSGT: 4, 9, 21, 26, 27,35For use with pages 51–58TEST TAKING STRATEGY1. Multiple ChoiceMake sure you are familiar with the directions beforetaking a standardized test. This way, you do not need toworry about the directions during the test.Find the perimeter of thefigure.7. Multiple ChoiceFind the area of the figure.A 18.84 square units7B8C14D16E3035B9.42 square unitsC28.26 square unitsy1D 56.52 square units2. Multiple ChoiceFind the circumference ofthe circle. sUse p 3.14.dE188.74 square unitsxA18.84 ftB37.68 ftC113.04 ftFind the area of therectangle defined by As2, 1d, Bs2, 4d, Cs6, 4dand Ds6, 1d.D37.68 ft2A7 square unitsB14 square unitsC24 square unitsD12 square unitsE9 square unitsE113.048. Multiple Choice6 ftft23. Multiple ChoiceFind the area of a squarewith a side of 7 inches.AD14 in.49in.2in.2B28E28 in.C49 in.4. Multiple ChoiceFind the area of a trianglewith a base of 8 m and a height of 4 m.AD19 mB16 mE32m212m2C16m25. Multiple ChoiceFind the area of a circlewith a radius of 9 meters. sUse p 3.14.dA28.26 m2B28.26 mC56.52m2D56.52 mE254.34 m29. Multiple ChoiceA square with an area of64 square inches has a perimeter of? .A64 in.B16 in.D128 in.Ecannot be determinedC32 in.10. Multiple ChoiceA triangle has an area of72 square feet and a height of 9 feet. Findits base.A16 ftB8 ftD9 ftE34 ftC32 ft11. Multi-Step ProblemA rectangular windowpane is 40 inches by 50 inches.a. Find the area of the window pane.b. Find the perimeter of the window pane.6. Multiple Choice50.24cm2B25.12cm2C401.92 cm2D200.96 cm2E100.48 cm2AFind the area of the figure.Copyright McDougal Littell Inc.All rights reserved.16 cmc. A frame around the window pane is1.5 inches wide. Find the area and perimeter of the window pane, including theframe. With the frame, by what percentdid the area increase?GeometryGeorgia Standardized Test Practice Workbook7Chapter 1A

LESSON2.1GA QCC: 5, 6, 9Standardized Test PracticeFor use with pages 71–78TEST TAKING STRATEGYWhen checking your work, try to use a method other thanthe one you originally used to get your answer. If you usethe same method, you may make the same mistake twice.1. Multiple ChoiceWhat is the if-then form of“A group is a dozen if it has 12 objects?”ABCDEIf a group does not have 12 objects, thenit is not a dozen.If a group is not a dozen, then it does nothave 12 objects.If a group has 12 objects, then it is adozen.A group is a dozen if and only if it has12 objects.None of the aboveWhat is the inverse of“If water is ice, then the water’s temperatureis 328F?”Chapter 22. Multiple ChoiceABCDEIf water’s temperature is 328F, then it isice.If water is not ice, then its temperature isnot 328F.If water’s temperature is not 328F, thenwater is not ice.Water is ice if and only if its temperatureis 328F.None of the above3. Multiple ChoiceWhat is the converse of “Ifyou are hungry, then you did not eat lunch?”ABCDEIf you did not eat lunch, then you arehungry.If you ate lunch, then you are not hungry.If you are not hungry, then you ate lunch.You are hungry if and only if you did noteat lunch.None of the above4. Multiple ChoiceWhat is the contrapositiveof “If x 5 3, then 5x 2 2 5 13?”8A5x 2 2 5 13 if and only if x 5 3.BIf x Þ 3, then 5x 2 2 Þ 13.CIf 5x 2 2 5 13, then x 5 3.GeometryGeorgia Standardized Test Practice WorkbookDIf 5x 2 2 Þ 13, then x Þ 3.ENone of the above5. Multiple ChoiceWhich of the followingstatements is not true?AIf x 5 4, then x2 5 16.BIf x3 5 227, then x 5 23.CIf x Þ 23, then x3 Þ 227.DIf x 5 2, then x2 5 4.EIf x2 5 4, then x 5 2.6. Multiple ChoiceUse the conditionalstatement “If an angle is obtuse, then theangle measures 988” to decide which of thefollowing are true.I. The statement is true.II. The converse of the statement is true.III. The contrapositive of the statement istrue.A I onlyB II onlyCIII onlyEI and III7. Multi-Step ProblemDI and IIUse Postulate 8 toanswer parts (a)–(e).Postulate 8: Through any three noncollinear points there existsexactly one plane.a. Rewrite Postulate 8 in if-then form.b. Write the converse of Postulate 8.c. Write the inverse of Postulate 8.d. Write the contrapositive of Postulate 8.e. Critical ThinkingAre the statementsyou wrote in parts (a)–(d) true?Copyright McDougal Littell Inc.All rights reserved.

LESSON2.2GA QCC: 4, 6, 8Standardized Test PracticeFor use with pages 79–85TEST TAKING STRATEGYIf you find yourself spending too much time on one testquestion and getting frustrated, move to the next question.You can revisit a difficult problem later with a freshperspective.Given that /2 /4 and/2 /5, which statement about the diagramis not true?1. Multiple Choice4. Multiple ChoiceWhich of the followingis true about the conditional statement “Ifm/1 5 308 and the m/2 5 1508, then theangles are supplementary?”A/5 /4B/6 and /2 aresupplementary.C/8 and /5 aresupplementary.D/1 /8AIBIIE/1 and /3 are supplementary.DI and IIEI, II, and III1 25 63 47 8What is the biconditionalform of the statement “If a whitetail deer hasantlers, then it is a male deer?”BCDEA whitetail deer has no antlers if andonly if it is not a male deer.A whitetail deer has antlers if and only ifit is a male deer.If a whitetail deer has no antlers, then itis not a male deer.If a whitetail deer is male, then it hasantlers.None of the above3. Multiple ChoiceWhich one of the following statements cannot be written as a truebiconditional statement?AIf the sum of two angles is 908, then theyare complementary.BIf two angles have the same measurement, then they are congruent.If 5x 1 7 5 22, then x 5 3.CDEIf two angles are linear, then they aresupplementary.If y lies between x and z, thenxy 1 yz 5 xz.Copyright McDougal Littell Inc.All rights reserved.CIII5. Multiple ChoiceWhich statement belowwould be a true biconditional statement?AIf /ABC measures 908, then it is a rightangle.BIf two angles are adjacent, then theyshare a common side.If two squares have the same diagonallength, then they have equal sides.A and CAll of the aboveCDEQuantitative ComparisonIn Exercises 6and 7, choose the statement below that istrue about the given quantities.AThe quantity in column A is greater.BThe quantity in column B is greater.CThe two quantities are equal.DThe relationship cannot be determinedfrom the given information.Column AColumn B6.The number of linescreated by the intersection of two planesThe number of linesthat can be drawnthrough any one point7.The sum of two supplementary anglesThe sum of twoadjacent anglesGeometryGeorgia Standardized Test Practice Workbook9Chapter 22. Multiple ChoiceAI. The statement is true.II. The converse is true.III. The statement can be written as a truebiconditional.

LESSONGA QCC: 4, 5, 62.3Standardized Test PracticeGHSGT: 4For use with pages 87–95TEST TAKING STRATEGYIt is important to remember that your SAT score will notsolely determine your acceptance into a college or university. Do not put added pressure on yourself to do well. If youare not satisfied with your SAT score, remember you cantake it again.Multiple Choice For Exercises 1–3, let pbe “It is raining,” let q be “It is thundering,” and let r be “We cannot swim.”1. What is q p?ABCDChapter 2EIf it is raining, then it is thundering.If it is raining, then we cannot swim.If it is thundering, then it is raining.If it is thundering, then we cannot swim.If it is not raining, then it is notthundering.2. What is the converse of p q?ABCDEIf it is thundering, then it is raining.If it is not raining, then it is notthundering.If it is not thundering, then it is notraining.If it is not thundering, then it is raining.If it is thundering, then it is not raining.3. What is the contrapositive of r q?ABCDEIf it is thundering, then we cannot swim.If we can swim, then it is not thundering.If we cannot swim, then it is notthundering.If we can swim, then it is thundering.If it is not thundering, then we can swim.4. Multiple Choicecould beABCDE10?The statement p r.the inverse of r pthe inverse of r pthe contrapositive of r pthe converse of r pthe contrapositive of r pGeometryGeorgia Standardized Test Practice Workbook5. Multiple ChoiceWhich law of logic allowsthe conclusion given the true statement?“If it is Saturday, then Nina’s family rentsmovies. Today is Saturday, therefore Ninaconcludes her family will rent movies.”ALaw of DetachmentBLaw of SyllogismCInductive reasoningDDeductive reasoningENone of the above6. Multiple ChoiceWhich law of logic allowsthe c

Georgia Geometry Standardized Test Practice Workbook The Standardized Test Practice Workbook provides practice exercises for every lesson in a standardized test format. Included are multiple-choice, quantitative-comparison, and multi-step problems. The Standardized Test Practice for every lesson is correlated to the Georgia

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