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Geometry: All-In-One Answers Version BName Class DateLesson 1-1Example.Patterns and Inductive ReasoningLesson Objective1Name Class Date2 Using Inductive Reasoning Make a conjecture about the sum of the cubesNAEP 2005 Strand: GeometryUse inductive reasoning to makeconjecturesof the ﬁrst 25 counting numbers.Find the ﬁrst few sums. Notice that each sum is a perfect square and thatthe perfect squares form a pattern.Topic: Mathematical ReasoningLocal Standards:3131 31 31 31 Vocabulary.conjectureis a conclusion you reach using inductive reasoning.A counterexample is an example for which the conjecture is incorrect.All rights reserved.AAll rights reserved.Inductive reasoning is reasoning based on patterns you observe.half2 296 248 the sum of the first 25 counting numbers, or (1 2 3 . . . 25) 2.2the preceding term. The next two 24and 24 212.Quick Check.1. Find the next two terms in each sequence.a. 1, 2, 4, 7, 11, 16, 22,29 ,37b. Monday, Tuesday, Wednesday,,.,ThursdayFriday,.c.,,.Answers may vary. Sample:Geometry Lesson 1-1Daily Notetaking Guide Pearson Education, Inc., publishing as Pearson Prentice Hall.terms are 48 192 Pearson Education, Inc., publishing as Pearson Prentice Hall.Each term isAll rights reserved.212(1 2)2(1 2 3)2(1 2 3 4)2(1 2 3 4 5)the sum of the cubes of the first 25 counting numbers equals the square ofUse the pattern to find the next two terms in the sequence.384, 192, 96, 48, . . .L1Quick Check.2. Make a conjecture about the sum of the ﬁrst 35 odd numbers. Use yourcalculator to verify your conjecture.1 1 1 3 4 221 3 5 9 321 3 5 7 16 421 3 5 7 9 25 5212The sum of the first 35 odd numbers is 35 2, or 1225.L1Daily Notetaking GuideGeometry Lesson 1-13Name Class DateName Class DateLesson 1-2Example.Drawings, Nets, and Other Models2 Drawing a Net Draw a net for the ﬁgure with a square baseNAEP 2005 Strand: GeometryTopic: Dimension and Shapeand four isosceles triangle faces. Label the net with its dimensions.10cmLesson Objectives1 Make isometric and orthographicdrawings2 Draw nets for three-dimensionalfigures Pearson Education, Inc., publishing as Pearson Prentice Hall. 1 1 2 9 3 2 36 6 2 100 10 2 225 15 The sum of the ﬁrst two cubes equals the square of the sum of the ﬁrsttwocounting numbers. The sum of the ﬁrst three cubes equals thesquare of the sum of the ﬁrst three counting numbers. This patterncontinues for the fourth and ﬁfth rows. So a conjecture might be thatExample.1 Finding and Using a Pattern Find a pattern for the sequence. 3842232332 33332 3 433332 3 4 5Think of the sides of the square base as hinges, and “unfold” theﬁgure at these edges to form a net. The base of each of the foursquareisosceles triangle faces is a side of the. Write in theknown dimensions.Local Standards:Vocabulary.8 cmorthographic drawingAll rights reserved.on isometric dot paper.Anis the top view, front view, and right-side view of a three-dimensional figure.A net is a two-dimensional pattern you can fold to form a three-dimensional figure.All rights reserved.An isometric drawing of a three-dimensional object shows a corner view of the figure drawnExample.8 cm10cmQuick Check.1 Orthographic Drawing Make an orthographic drawing of the isometric drawing at right.Orthographic drawings ﬂatten the depth of a ﬁgure. An orthographicthreedrawing showsviews. Becauseno edge of the isometric drawing is hidden in the top, front,and right views, all lines are solid.2. The drawing shows one possible net for the Graham Crackers box.htt RigonFrontTopRightQuick Check.1. Make an orthographic drawing from this isometric drawing.FrontTop Pearson Education, Inc., publishing as Pearson Prentice Hall.Fr Pearson Education, Inc., publishing as Pearson Prentice Hall.14 cm20 cm7 cmAMAHGR KERSACCRAMAHGR KERSACCR20 cm7 cm14 cmDraw a different net for this box. Show the dimensions in your diagram.Answers may vary. Example:14 cm20 cmFrhtont RigRight7 cm4L1Geometry Lesson 1-2Daily Notetaking GuideAll-In-One Answers Version BL1L1Daily Notetaking GuideGeometry Lesson 1-2Geometry51

Geometry: All-In-One Answers Version B (continued)Name Class DateLesson 1-31A plane is a flat surface that has no thickness.Points, Lines, and PlanesLesson Objectives2Name Class DateNAEP 2005 Strand: GeometryUnderstand basic terms of geometryUnderstand basic postulates ofgeometryBCAPlane ABCTwo points or lines are coplanar if they lie on the same plane.Topic: Dimension and ShapeA postulate or axiom is an accepted statement of fact.Local Standards:Examples.Vocabulary and Key Concepts.name three points that are collinear and three pointsthat are not collinear.Postulate 1-1tLine t is the only line that passes through points A and B .BAPointsAll rights reserved.All rights reserved.Through any two points there is exactly one line.*AE )BCE*,Z, andWlie on a line, so they aremZY2 Using Postulate 1-4 Shade the plane that contains X, Y, and Z.Postulate 1-2AYcollinear.)and BD intersect at C .YVPostulate 1-4Through any three noncollinear points there is exactly one plane.A point is a location.is the set of all points.SpaceA line is a series of points that extends in two opposite directionswithout end.tb. Name line m in three different ways.*)*)* )Answers may vary. Sample: ZW , WY , YZ .2. a. Shade plane VWX.Zb. Name a point that is coplanarwith points V, W, and X.YYVXWare points that lie on the same line.Collinear points6BAnoAll rights reserved.STPlane RST and plane STW intersect in ST .1. Use the ﬁgure in Example 1.a. Are points W, Y, and X collinear? Pearson Education, Inc., publishing as Pearson Prentice Hall.* )RT WS Pearson Education, Inc., publishing as Pearson Prentice Hall.If two planes intersect, then they intersect in exactly one line.XWQuick Check.Postulate 1-3WZPoints X, Y, and Z are the vertices of one of the four triangularfaces of the pyramid. To shade the plane, shade the interior ofthe triangle formed by X , Y , and Z .If two lines intersect, then they intersect in exactly one point.DX1 Identifying Collinear Points In the ﬁgure at right,Geometry Lesson 1-3Daily Notetaking GuideL1Daily Notetaking GuideL1Geometry Lesson 1-37Name Class DateName Class DateLesson 1-4Examples.1 Naming Segments and Rays Name the segments and rays in the ﬁgure.NAEP 2005 Strand: GeometryTopic: Relationships Among Geometric FiguresThe labeled points in the ﬁgure are A, B, and C.Local Standards:A segment is a part of a line consisting of two endpoints and all pointsbetween them. A segment is named by its two endpoints. So theBA (or AB)segments areand.BC (or CB)BA ray is a part of a line consisting of one endpoint and all the points ofthe line on one side of that endpoint. A ray is named by its endpoint ﬁrst, followed) .)by any other point on the ray. So the rays areandBABCVocabulary.Segment ABABABAEndpointEndpoint)is the part of a line consisting of one endpoint andrayRay YXYXall the points of the line on one side of the endpoint.XYEndpointAll rights reserved.endpoints and all points between them.All rights reserved.A segment is the part of a line consisting of two)RQand)RRSParallel planesAJparallel AB and CG are to EF.skewlines.Fare planes that do not intersect.GDAB is GHBPlane ABCD isparallelto plane GHIJ.IC Pearson Education, Inc., publishing as Pearson Prentice Hall.E . If the walls of your classroom))1. Critical Thinking Use the ﬁgure in Example 1. CB and BC form a line. Arethey opposite rays? Explain. Pearson Education, Inc., publishing as Pearson Prentice Hall.CBwalls are parts of parallel planes. If the ceiling andoppositeQuick Check.are opposite rays.Skew lines are noncoplanar; therefore, they are not parallel and do not intersect.Hdo not intersectare vertical,Sare coplanar lines that do not intersect.DPlanes are parallel if theyfloor of the classroom are level, they are parts of parallel planes.Qendpoint.AC2 Identifying Parallel Planes Identify a pair of parallel planes in your classroom.Opposite rays are two collinear rays with the sameParallel linesA Pearson Education, Inc., publishing as Pearson Prentice Hall.Segments, Rays, Parallel Lines and PlanesLesson Objectives1 Identify segments and rays2 Recognize parallel linesNo; they do not have the same endpoint.2. Use the diagram to the right.a. Name three pairs of parallel planes.PSWT RQVU, PRUT SQVW, PSQR TWVUSQRPW* )b. Name a line that is parallel to PQ .TVU* )TVc. Name a line that is parallel to plane QRUV.* )Answers may vary. Sample: PS82Geometry Lesson 1-4GeometryDaily Notetaking GuideL1L1Daily Notetaking GuideGeometry Lesson 1-4All-In-One Answers Version B9L1

Geometry: All-In-One Answers Version B (continued)Name Class DateLesson 1-5Examples.Measuring SegmentsLesson Objectives1Name Class Date1 Using the Segment Addition Postulate If AB 25,NAEP 2005 Strand: MeasurementFind the lengths of segments2x 6ﬁnd the value of x. Then ﬁnd AN and NB.Local Standards: NBAN(Vocabulary and Key Concepts.) (2x 6 AB3x that the distance between any two points is the absolute value of the difference of thecorresponding numbers.Simplify the left side.24Subtract 1 from each side.x 8All rights reserved.All rights reserved.correspondence with the real numbers soSubstitute. 1 253x( ) 6 NB x 7 ( 8 ) 7 AN 2x 6 2 8AN and NB 1015BSegment Addition Postulate) 25x 7Postulate 1-5: Ruler PostulateThe points of a line can be put into one-to-onex 7ANUse the Segment Addition Postulate (Postulate 1-6) to write an equation.Topic: Measuring Physical AttributesDivide each side by 3 .10Substitute 8 for x.15, which checks because the sum equals 25.Postulate 1-6: Segment Addition PostulateIf three points A, B, and C are collinear and B2 Finding Lengths M is the midpoint of RT.ABis between A and C, then AB BC AC.8x 365x 9Find RM, MT, and RT.CRMTUse the deﬁnition of midpoint to write an equation.RM A coordinate is a point’s distance and direction from zero on a number line.All rights reserved.RAB 5 u aQABabubacoordinate of Acoordinate of BCongruent (艑) segments are segments with the same length.2 cmABADC 2 cmC BAB CD ABCDDmidpoint Pearson Education, Inc., publishing as Pearson Prentice Hall.the length of AB Pearson Education, Inc., publishing as Pearson Prentice Hall.5x 95x segments.B AB MT(RM 5x 9 5(MT 8x 36 81515Substitute. 8xRT RM MT 84RM and MT are each36AddSubtract x) 9 ) 36 midpointDefinition of 8x 3645 3 x15to each side.5xfrom each side.Divide each side by 3 .84Substitute8416815for x.Segment Addition, which is half of168Postulate, the length of RT.Quick Check.1. EG 100. Find the value of x. Then ﬁnd EF and FG.4x – 20x 15, EF 40; FG 60A midpoint is a point that divides a segment into two congruentA45E2x 30FGC2. Z is the midpoint of XY, and XY 27. Find XZ.BC13.510Geometry Lesson 1-5Daily Notetaking GuideL1Name Class DateLesson 1-6 Pearson Education, Inc., publishing as Pearson Prentice Hall.Examples.1 Naming Angles Name the angle at right in four ways.NAEP 2005 Strand: MeasurementTopic: Measuring Physical Attributes m BOCAB m AOC.0180m AOB m BOC 180T 1 Q TBQ90x5x x x angle9088Substitute 42for m ABC.m 2 46Subtract42Postulatefor m 1 and1882Bfrom each side.Cl2, lDECA O CrightAngle Addition m 2 1. a. Name CED two other ways.Bare the sides of the angle and the endpoint is the vertex of the angle.0,x,42Quick Check.If AOC is a straight angle, thenAn angle ( ) is formed by two rays with the same endpoint. The raysanglem 1 m 2 m ABCBBacuteAOO Cx All rights reserved.40140301502016 017 010Dobtuse90angle,x,straight anglex 5 180180 Pearson Education, Inc., publishing as Pearson Prentice Hall.AOB13050y Pearson Education, Inc., publishing as Pearson Prentice Hall.m 1206010Postulate 1-8: Angle Addition PostulateIf point B is in the interior of AOC, then7017 0A80x20.901AUse the Angle Addition Postulate (Postulate 1-8) to solve.16 0)7 0 10 06 0 11 02050 0 1310 0 110All rights reserved.C8001503014 04)mlCOD 5 u x 2 y u3G2 Using the Angle Addition Postulate Suppose that m 1 42and m ABC 88. Find m 2.b. If OC is paired with x and OD is paired with y,then.Finally, the name can be a point on one side, the vertex, and a pointon the other side of the angle: lAGC or lCGA .a. OA is paired with 0 and OB is paired with 180 .)lGThe name can be the vertex of the angle:Vocabulary and Key Concepts.)Cl3The name can be the number between the sides of the angle:Local Standards:Postulate 1-7: Protractor Postulate))Let OA and OB be opposite rays in a plane.) )OA , OB , and all the rays with endpoint O that can* )be drawn on one side of AB can be paired with thereal numbers from 0 to 180 so that11Geometry Lesson 1-5Name Class DateMeasuring AnglesLesson Objectives1 Find the measures of angles2 Identify special angle pairsDaily Notetaking GuideL1b. Critical Thinking Would it be correct to name any of theangles E? Explain.No, 3 angles have E for a vertex, so youneed more information in the name todistinguish them from one another.G2. If m DEG 145, ﬁnd m GEF.35DEFAn acute angle has measurement between 0 and 90 .A right angle has a measurement of exactly 90 .Anobtuse anglehas measurement between 90 and 180 .A straight angle has a measurement o