Transcription
GeometryChapter 1Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.Study Guide and Intervention WorkbookSkills Practice WorkbookPractice WorkbookReading to Learn Mathematics 7-861061-3ANSWERS FOR WORKBOOKS The answers for Chapter 1 of these workbookscan be found in the back of this Chapter Resource Masters booklet.Copyright by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced onlyfor classroom use; be provided to students, teachers, and families without charge;and be used solely in conjunction with Glencoe’s Geometry. Any other reproduction,for use or sale, is prohibited without prior written permission of the publisher.Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027ISBN: 0-07-846589-31 2 3 4 5 6 7 8 9 10 009 11 10 09 08 07 06 05 04 03GeometryChapter 1 Resource Masters
ContentsVocabulary Builder . . . . . . . . . . . . . . . . viiLesson 1-6Study Guide and Intervention . . . . . . . . . 31–32Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 33Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Reading to Learn Mathematics . . . . . . . . . . . 35Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 36Lesson 1-1Study Guide and Intervention . . . . . . . . . . . 1–2Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 3Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Reading to Learn Mathematics . . . . . . . . . . . . 5Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Chapter 1 rLesson 1-2Study Guide and Intervention . . . . . . . . . . . 7–8Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 9Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Reading to Learn Mathematics . . . . . . . . . . . 11Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 12Lesson 1-3Study Guide and Intervention . . . . . . . . . 13–14Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 15Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Reading to Learn Mathematics . . . . . . . . . . . 17Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Test, Form 1 . . . . . . . . . . . . . . 37–381 Test, Form 2A . . . . . . . . . . . . . 39–401 Test, Form 2B . . . . . . . . . . . . . 41–421 Test, Form 2C . . . . . . . . . . . . . 43–441 Test, Form 2D . . . . . . . . . . . . . 45–461 Test, Form 3 . . . . . . . . . . . . . . 47–481 Open-Ended Assessment . . . . . . . 491 Vocabulary Test/Review . . . . . . . . 501 Quizzes 1 & 2 . . . . . . . . . . . . . . . . 511 Quizzes 3 & 4 . . . . . . . . . . . . . . . . 521 Mid-Chapter Test . . . . . . . . . . . . . 531 Cumulative Review . . . . . . . . . . . . 541 Standardized Test Practice . . . 55–56Standardized Test PracticeStudent Recording Sheet . . . . . . . . . . . . . . A1Lesson 1-4Study Guide and Intervention . . . . . . . . . 19–20Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 21Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Reading to Learn Mathematics . . . . . . . . . . . 23Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 24ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A29Lesson 1-5Study Guide and Intervention . . . . . . . . . 25–26Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 27Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Reading to Learn Mathematics . . . . . . . . . . . 29Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Glencoe/McGraw-HilliiiGlencoe Geometry
Teacher’s Guide to Using theChapter 1 Resource MastersThe Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 1 Resource Masters includes the core materials neededfor Chapter 1. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.All of the materials found in this booklet are included for viewing and printing in theGeometry TeacherWorks CD-ROM.Vocabulary BuilderPracticePages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.WHEN TO USE Give these pages tostudents before beginning Lesson 1-1.Encourage them to add these pages to theirGeometry Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.Study Guide and InterventionEach lesson in Geometry addresses twoobjectives. There is one Study Guide andIntervention master for each objective.WHEN TO USE Use these masters asWHEN TO USE This master can be usedreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.as a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.Skills PracticeThere is one master foreach lesson. These provide computationalpractice at a basic level.EnrichmentThere is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.WHEN TO USE These masters can beused with students who have weakermathematics backgrounds or needadditional reinforcement.WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened. Glencoe/McGraw-HillivGlencoe Geometry
Assessment OptionsIntermediate AssessmentThe assessment masters in the Chapter 1Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use. Four free-response quizzes are includedto offer assessment at appropriateintervals in the chapter. A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.Chapter AssessmentCHAPTER TESTSContinuing Assessment Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents. The Cumulative Review providesstudents an opportunity to reinforce andretain skills as they proceed throughtheir study of Geometry. It can also beused as a test. This master includesfree-response questions. Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations. The Standardized Test Practice offerscontinuing review of geometry conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiplechoice, grid-in, and short-responsequestions. Bubble-in and grid-in answersections are provided on the master. Forms 2C and 2D are composed of freeresponse questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills. Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.Answers Page A1 is an answer sheet for theStandardized Test Practice questionsthat appear in the Student Edition onpages 58–59. This improves students’familiarity with the answer formats theymay encounter in test taking.All of the above tests include a freeresponse Bonus question. The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment. The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red. A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunction with one of the chapter tests or as areview worksheet. Glencoe/McGraw-Hill Full-size answer keys are provided forthe assessment masters in this booklet.vGlencoe Geometry
NAME DATE1PERIODReading to Learn MathematicsThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 1.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Geometry Study Notebook to review vocabulary at the end of the chapter.Vocabulary TermFoundon PageDefinition/Description/Exampleacute angle adjacent anglesuh·JAY·suhntangleangle bisector collinearkoh·LIN·ee·uhrcomplementary angles congruentkuhn·GROO·uhnt coplanarkoh·PLAY·nuhrline segmentlinear pair(continued on the next page) Glencoe/McGraw-HillviiGlencoe GeometryVocabulary BuilderVocabulary Builder
NAME DATE1PERIODReading to Learn MathematicsVocabulary BuilderVocabulary Term(continued)Foundon PageDefinition/Description/Examplemidpointobtuse angleperimeterperpendicular lines polygonPAHL·ee·gahnrayright anglesegment bisectorsupplementary anglesvertical angles Glencoe/McGraw-HillviiiGlencoe Geometry
NAME DATE1-1PERIODStudy Guide and InterventionPoints, Lines, and PlanesName Points, Lines, and PlanesIn geometry, a point is a location, a line containspoints, and a plane is a flat surface that contains points and lines. If points are on the sameline, they are collinear. If points on are the same plane, they are coplanar.ExampleUse the figure to name each of the following. Aa. a line containing point ADBThe line can be named as . Also, any two of the threepoints on the line can be used to name it. AB , AC , or BCCLesson 1-1Nb. a plane containing point DThe plane can be named as plane N or can be named using threenoncollinear points in the plane, such as plane ABD, plane ACD, and so on.ExercisesRefer to the figure. A1. Name a line that contains point A.Cm2. What is another name for lineDBEPm?3. Name a point not on AC .4. Name the intersection of AC and DB .5. Name a point not on line or lineDraw and label a plane is in plane6. ABm.Q for each relationship.SQ.XA at P.7. ST intersects ABPTQBY 8. Point X is collinear with points A and P.9. Point Y is not collinear with points T and P.10. Line contains points X and Y. Glencoe/McGraw-Hill1Glencoe Geometry
NAME DATE1-1PERIODStudy Guide and Intervention(continued)Points, Lines, and PlanesPoints, Lines, and Planes in SpaceSpace is a boundless, three-dimensional set ofall points. It contains lines and planes.Examplea. How many planes appear in the figure?There are three planes: planeOPNBN , plane O, and plane P.Ab. Are points A, B, and D coplanar?Yes. They are contained in planeDO.CExercisesRefer to the figure.A1. Name a line that is not contained in planeN.BC2. Name a plane that contains point B.NDE3. Name three collinear points.Refer to the figure.AB4. How many planes are shown in the figure?DGCHI5. Are points B, E, G, and H coplanar? Explain.FEJ6. Name a point coplanar with D, C, and E.Draw and label a figure for each relationship.7. Planes9. Line t contains point H and lineplane N.Glencoe/McGraw-HillMs8. Line r is in plane N , line s is in planeintersect at point J. tM andN intersect in HJ .M , and lines r and sNHJrt does not lie in plane M or2Glencoe Geometry
NAME DATE1-1PERIODSkills PracticePoints, Lines, and PlanesRefer to the figure.A1. Name a line that contains point D.BpDnCG2. Name a point contained in line n.4. Name the plane containing linesLesson 1-13. What is another name for line p ?n and p.Draw and label a figure for each relationship.5. Point K lies on RT .K6. PlaneJ contains line s.TRsJ lies in plane B and contains7. YPpoint C, but does not contain point H.YC8. Lines q andin plane U.HfqPUBRefer to the figure.f intersect at point ZZF9. How many planes are shown in the figure?DEA10. How many of the planes contain points F and E?CWB11. Name four points that are coplanar.12. Are points A, B, and C coplanar? Explain. Glencoe/McGraw-Hill3Glencoe Geometry
NAME DATE1-1PERIODPracticePoints, Lines, and PlanesRefer to the figure.jM1. Name a line that contains points T and P.PSTRQNhg2. Name a line that intersects the plane containingpoints Q, N, and P. .3. Name the plane that contains TN and QRDraw and label a figure for each relationship. and CG intersect at point M4. AKin plane T.ATCM5. A line contains L( 4, 4) and M(2, 3). Lineq is in the same coordinate plane but does . Line q contains point N.not intersect LMyGKMqxONLRefer to the figure.TQ6. How many planes are shown in the figure?W7. Name three collinear points.A8. Are points N, R, S, and W coplanar? Explain.SXMPRNVISUALIZATION Name the geometric term(s) modeled by each object.9.10.11.tip of pinSTOP12. a car antenna Glencoe/McGraw-Hillstrings13. a library card4Glencoe Geometry
NAME DATE1-1PERIODReading to Learn MathematicsPoints, Lines, and PlanesPre-ActivityWhy do chairs sometimes wobble?Read the introduction to Lesson 1-1 at the top of page 6 in your textbook. How many ways can you do this if you keep the pencil points in the sameposition? How will your answer change if there are four pencil points?Reading the Lesson1. Complete each sentence.a. Points that lie on the same lie are calledpoints.b. Points that do not lie in the same plane are calledpoints.c. There is exactly onethrough any two points.d. There is exactly onethrough any three noncollinear points.2. Refer to the figure at the right. Indicate whether eachstatement is true or false.DUa. Points A, B, and C are collinear.Cb. The intersection of plane ABC and linec. Line and linem is point P. BPAm do not intersect.md. Points A, P,and B can be used to name planeU.e. Line lies in plane ACB.3. Complete the figure at the right to show the followingrelationship: Lines , m, and n are coplanar and lie inplane Q. Lines and m intersect at point P. Line nintersects line m at R, but does not intersect line . QnPRmHelping You Remember4. Recall or look in a dictionary to find the meaning of the prefix co-. What does this prefixmean? How can it help you remember the meaning of collinear? Glencoe/McGraw-Hill5Glencoe GeometryLesson 1-1 Find three pencils of different lengths and hold them upright on yourdesk so that the three pencil points do not lie along a single line. Can youplace a flat sheet of paper or cardboard so that it touches all three pencilpoints?
NAME DATE1-1PERIODEnrichmentPoints and Lines on a MatrixA matrix is a rectangular array of rows and columns. Points andlines on a matrix are not defined in the same way as in Euclideangeometry. A point on a matrix is a dot, which can be small orlarge. A line on a matrix is a path of dots that “line up.” Betweentwo points on a line there may or may not be other points. Threeexamples of lines are shown at the upper right. The broad line canbe thought of as a single line or as two narrow lines side by side.Dot-matrix printers for computers used dots to form characters.The dots are often called pixels. The matrix at the right showshow a dot-matrix printer might print the letter P.Draw points on each matrix to create the given figures.1. Draw two intersecting lines that havefour points in common.2. Draw two lines that cross but haveno common points.3. Make the number 0 (zero) so that itextends to the top and bottom sidesof the matrix.4. Make the capital letter O so that itextends to each side of the matrix.5. Using separate grid paper, make dot designs for several other letters. Which were theeasiest and which were the most difficult? Glencoe/McGraw-Hill6Glencoe Geometry
NAME DATE1-2PERIODStudy Guide and InterventionLinear Measure and PrecisionMeasure Line SegmentsA part of a line between two endpoints is called a linesegment. The lengths of M N and R S are written as MN and RS. When you measure asegment, the precision of the measurement is half of the smallest unit on the ruler.Example 2Find the length of M N .MNcm123Find the length of R S .R4Sin.The long marks are centimeters, and theshorter marks are millimeters. The length of NM is 3.4 centimeters. The measurement isaccurate to within 0.5 millimeter, so M N isbetween 3.35 centimeters and 3.45centimeters long.12The long marks are inches and the shortmarks are quarter inches. The length of R S 34is about 1 inches. The measurement isaccurate to within one half of a quarter inch,1858 S is between 1 inches andor inch, so R78Lesson 1-2Example 11 inches long.ExercisesFind the length of each line segment or object.1. Acm2. SB123Tin.3.14.in.12cm123Find the precision for each measurement. 5. 10 in.6. 32 mm7. 44 cm8. 2 ft9. 3.5 mm10. 2 ydGlencoe/McGraw-Hill127Glencoe Geometry
NAME DATE1-2PERIODStudy Guide and Intervention(continued)Linear Measure and PrecisionOn PQ, to say that point M isbetween points P and Q means P, Q, and M are collinearand PM MQ PQ.On AC, AB BC 3 cm. We can say that the segments arecongruent, or A B B C . Slashes on the figure indicate whichsegments are congruent.Calculate MeasuresExample 11.2 cmDBAExample 2Find EF.QCFind x and AC.2x 51.9 cmEMPFxA2xBCCalculate EF by adding ED and DF.B is between A and C.ED DF EF1.2 1.9 EF3.1 EFAB BC ACx 2x 2x 53x 2x 5x 5AC 2x 5 2(5) 5 15Therefore, E F is 3.1 centimeters long.ExercisesFind the measurement of each segment. Assume that the art is not drawn to scale.1. R T 2.0 cmR2. B C 2.5 cmS3. X Z T3 –21 in.3–4XYin.6 in.A2 –43in. B4. W X 6 cmWZCXYFind x and RS if S is between R and T.5. RS 5x, ST 3x, and RT 48.6. RS 2x, ST 5x 4, and RT 32.7. RS 6x, ST 12, and RT 72.8. RS 4x, R S S T , and RT 24.Use the figures to determine whether each pair of segments is congruent.9. A B and C D 10. X Y and Y Z 11 cmA5 cmBXD5 cm11 cm3x 5CY Glencoe/McGraw-Hill85x 19x2ZGlencoe Geometry
NAME DATE1-2PERIODSkills PracticeLinear Measure and PrecisionFind the length of each line segment or object.1.2.cm12345in.12Find the precision for each measurement.125. 9 inches4. 12 centimetersLesson 1-23. 40 feetFind the measurement of each segment.6. N Q 7. A C 1–41 in.1in.QP8. G H 4.9 cmAN5.2 cmBF9.7 mmCGH15 mmFind the value of the variable and YZ if Y is between X and Z.9. XY 5p, YZ p, and XY 2510. XY 12, YZ 2g, and XZ 2811. XY 4m, YZ 3m, and XZ 4212. XY 2c 1, YZ 6c, and XZ 81Use the figures to determine whether each pair of segments is congruent.13. B E , C D 14. M P , N P B 2m C3mE 12 yd3m5mDGlencoe/McGraw-HillM12 yd15. W X , W Z PY10 yd5 ftNX99 ftZ5 ftWGlencoe Geometry
NAME DATE1-2PERIODPracticeLinear Measure and PrecisionFind the length of each line segment or object.1. E2.Fin.12cm12345Find the precision for each measurement.144. 7 inches3. 120 meters5. 30.0 millimetersFind the measurement of each segment.6. P S 7. A D 18.4 cmP2–83 in.4.7 cmQ8. W X SA1–41 in.CWXY89.6 cm100 cmDFind the value of the variable and KL if K is between J and L.9. JK 6r, KL 3r, and JL 2710. JK 2s, KL s 2, and JL 5s 10Use the figures to determine whether each pair of segments is congruent.11. T U , S W 12. A D , B C T 2 ft S2 ftA13. G F , F E 12.7 in.BG5x3 ftU3 ftWH6xD12.9 in.C14. CARPENTRY Jorge used the figure at the right to make a patternfor a mosaic he plans to inlay on a tabletop. Name all of thecongruent segments in the figure.FEAFBECD Glencoe/McGraw-Hill10Glencoe Geometry
NAME DATE1-2PERIODReading to Learn MathematicsLinear Measure and PrecisionPre-ActivityWhy are units of measure important?Read the introduction to Lesson 1-2 at the top of page 13 in your textbook. The basic unit of length in the metric system is the meter. How manymeters are there in one kilometer? Do you think it would be easier to learn the relationships between thedifferent units of length in the customary system (used in the UnitedStates) or in the metric system? Explain your answer.Reading the LessonLesson 1-21. Explain the difference between a line and a line segment and why one of these can bemeasured, while the other cannot.2. What is the smallest length marked on a 12-inch ruler?What is the smallest length marked on a centimeter ruler?3. Find the precision of each measurement.a. 15 cmb. 15.0 cm4. Refer to the figure at the right. Which one of the followingstatements is true? Explain your answer. BA C D BA C D A4.5 cmDC4.5 cmB5. Suppose that S is a point on V W and S is not the same point as V or W. Tell whethereach of the following statements is always, sometimes, or never true.a. VS SWb. S is between V and W.c. VS VW SWHelping You Remember6. A good way to remember terms used in mathematics is to relate them to everyday wordsyou know. Give three words that are used outside of mathematics that can help youremember that there are 100 centimeters in a meter. Glencoe/McGraw-Hill11Glencoe Geometry
NAME DATE1-2PERIODEnrichmentPoints Equidistant from SegmentsThe distance from a point to a segment is zero if the point is on thesegment. Otherwise, it is the length of the shortest segment from thepoint to the segment.A figure is a locus if it is the set of all points that satisfy14a set of conditions. The locus of all points that are inchABfrom the segment AB is shown by two dashed segmentswith semicircles at both ends.1. Suppose A, B, C, and D are four different points, and consider the locusof all points x units from A B and x units from C D . Use any unit you findconvenient. The locus can take different forms. Sketch at least threepossibilities. List some of the things that seem to affect the form ofthe locus.ACBXYRBDAYAXCPCSDBQD2. Conduct your own investigation of the locus of pointsequidistant from two segments. Describe your results on aseparate sheet of paper. Glencoe/McGraw-Hill12Glencoe Geometry
NAME DATE1-3PERIODStudy Guide and InterventionDistance and MidpointsDistance Between Two PointsDistance on a Number LineAPythagorean Theorem:BaDistance in the Coordinate Planeya2 b2 c2bB(1, 3)Distance Formula:AB b a or a b d (x2 x1)2 (y2 y1)2A(–2, –1)xOC (1, –1)Find AB.A 5 4 3 2 1B012AB ( 4) 2 6 63Example 2Find the distance betweenA( 2, 1) and B(1, 3).Pythagorean Theorem(AB)2 (AC)2 (BC)2(AB)2 (3)2 (4)2(AB)2 25AB 25 5Distance Formulad (x2 x1)2 (y2 y1)2AB (1 ( 2))2 (3 ( 1))2 AB (3)2 (4)2 25 5ExercisesUse the number line to find each measure.1. BD2. DG3. AF4. EF5. BG6. AG7. BE8. DEABC–10 –8 –6 –4 –2DE0F2G468Use the Pythagorean Theorem to find the distance between each pair of points.9. A(0, 0), B(6, 8)11. M(1, 2), N(9, 13)10. R( 2, 3), S(3, 15)12. E( 12, 2), F( 9, 6)Use the Distance Formula to find the distance between each pair of points.13. A(0, 0), B(15, 20)14. O( 12, 0), P( 8, 3)15. C(11, 12), D(6, 2)16. E( 2, 10), F( 4, 3) Glencoe/McGraw-Hill13Glencoe GeometryLesson 1-3Example 1
NAME DATE1-3PERIODStudy Guide and Intervention(continued)Distance and MidpointsMidpoint of a SegmentIf the coordinates of the endpoints of a segment are a and b,Midpoint on aNumber Linea b.then the coordinate of the midpoint of the segment is 2If a segment has endpoints with coordinates (x1, y1) and (x2, y2),Midpoint on aCoordinate PlaneExample 1P x x2y y2 1212 then the coordinates of the midpoint of the segment are , .Find the coordinate of the midpoint of P Q .Q–3 –2 –1012The coordinates of P and Q are 3 and 1. 3 12 22 Q , then the coordinate of M is or 1.If M is the midpoint of PExample 2M is the midpoint of P Q for P( 2, 4) and Q(4, 1). Find thecoordinates of M. x x2y y2 22 44 12 1212 M , , or (1, 2.5)ExercisesUse the number line to find the coordinate ofthe midpoint of each segment.ABC–10 –8 –6 –4 –21. C E 2. D G 3. A F 4. E G 5. A B 6. B G 7. B D 8. D E DEF02G468Find the coordinates of the midpoint of a segment having the given endpoints.9. A(0, 0), B(12, 8)10. R( 12, 8), S(6, 12)11. M(11, 2), N( 9, 13)12. E( 2, 6), F( 9, 3)13. S(10, 22), T(9, 10)14. M( 11, 2), N( 19, 6) Glencoe/McGraw-Hill14Glencoe Geometry
NAME DATE1-3PERIODSkills PracticeDistance and MidpointsUse the number line to find each measure.1. LN2. JL3. KN4. MNJ–6K–4L–202M46N810Use the Pythagorean Theorem to find the distance between each pair of points.5.6.yySGOxOxFD8. C( 3, 1), Q( 2, 3)7. K(2, 3), F(4, 4)Use the Distance Formula to find the distance between each pair of points.10. W( 2, 2), R(5, 2)11. A( 7, 3), B(5, 2)Lesson 1-39. Y(2, 0), P(2, 6)12. C( 3, 1), Q(2, 6)Use the number line to find the coordinateof the midpoint of each segment.13. D E 14. B C 15. B D 16. A D A–6–4B–2C02D46E81012Find the coordinates of the midpoint of a segment having the given endpoints.17. T(3, 1), U(5, 3)18. J( 4, 2), F(5, 2)Find the coordinates of the missing endpoint given that P is the midpoint of N Q .19. N(2, 0), P(5, 2) Glencoe/McGraw-Hill20. N(5, 4), P(6, 3)1521. Q(3, 9), P( 1, 5)Glencoe Geometry
NAME DATE1-3PERIODPracticeDistance and MidpointsUse the number line to find each measure.1. VW2. TV3. ST4. SVS–10–8–6TU–4–2V0W2468Use the Pythagorean Theorem to find the distance between each pair of points.5.6.yySZOOxxMEUse the Distance Formula to find the distance between each pair of points.7. L( 7, 0), Y(5, 9)8. U(1, 3), B(4, 6)Use the number line to find the coordinateof the midpoint of each segment.9. R T 10. Q R 11. S T 12. P R P–10Q–8–6R–4–2S0T246Find the coordinates of the midpoint of a segment having the given endpoints.13. K( 9, 3), H(5, 7)14. W( 12, 7), T( 8, 4)Find the coordinates of the missing endpoint given that E is the midpoint of D F .15. F(5, 8), E(4, 3)16. F(2, 9), E( 1, 6)17. D( 3, 8), E(1, 2)18. PERIMETER The coordinates of the vertices of a quadrilateral are R( 1, 3), S(3, 3),T(5, 1), and U( 2, 1). Find the perimeter of the quadrilateral. Round to thenearest tenth. Glencoe/McGraw-Hill16Glencoe Geometry
NAME DATE1-3PERIODReading to Learn MathematicsDistance and MidpointsPre-ActivityHow can you find the distance between two points without a ruler?Read the introduction to Lesson 1-3 at the top of page 21 in your textbook. Look at the triangle in the introduction to this lesson. What is the special B in this triangle?name for A Find AB in this figure. Write your answer both as a radical and as adecimal number rounded to the nearest tenth.Reading the Lesson1. Match each formula or expression in the first column with one of the names in thesecond column.a. d (x2 x1)2 ( y2 y1)2i. Pythagorean Theorema b2b. ii. Distance Formula in the Coordinate Planec. XY a b iii. Midpoint of a Segment in the Coordinate Planed. c2 a2 b2iv. Distance Formula on a Number Line x x2y y21212 , e. v. Midpoint of a Segment on a Number Line2. Fill in the steps to calculate the distance between the points M(4, 3) and N( 2, 7).,d ( )2 ( )2MN ( )2 ( )2MN ()2 ()2MN MN ).Lesson 1-3Let (x1, y1) (4, 3). Then (x2, y2) (Find a decimal approximation for MN to the nearest hundredth.Helping You Remember3. A good way to remember a new formula in mathematics is to relate it to one you alreadyknow. If you forget the Distance Formula, how can you use the Pythagorean Theorem tofind the distance d between two points on a coordinate plane? Glencoe/McGraw-Hill17Glencoe Geometry
NAME DATE1-3PERIODEnrichmentLengths on a GridEvenly-spaced horizontal and vertical lines form a grid.You can easily find segment lengths ona grid if the endpoints are grid-lineintersections. For horizontal or verticalsegments, simply count squares. Fordiagonal segments, use the Pyth
Glencoe/McGraw-Hill iv Glencoe Geometry Teacher’s Guide to Using the Chapter 1 Resource Masters The Fast FileChapter Resource system allows you to conveniently file the resources you use most often. The Chapter 1 Resource Mastersincludes the core materials needed for Chapter 1. These material
