Geometry: All-In-One Answers Version B

1 Pearson Education, Inc., publishing as Pearson Prentice rights Answers Version BGeometryL1 geometry : All-In-One Answers Version BGeometryLesson 1-1 Daily Notetaking GuideL12 Pearson Education, Inc., publishing as Pearson Prentice rights reasoning isA is a conclusion you reach using inductive counterexample and Using a PatternFind a pattern for the the pattern to find the next two terms in the , 192, 96, 48,..Each term is the preceding term. The next twoterms are 48 and 24 .Quick the next two terms in each ,2,4,7,11,16,22,,,.. , Tuesday, Wednesday,,,..c.,,.. Answers may vary. Sample:3841929648 1 Name_____ Class_____ Date_____Lesson ObjectiveUse inductive reasoning to makeconjectures1 NAEP 2005 Strand:GeometryTopic:Mathematical ReasoningLocal Standards: _____Lesson 1-1 Patterns and Inductive Reasoningreasoning based on patterns you example for which the conjecture is 1-2 Daily Notetaking GuideL14 Name_____ Class_____ Date_____ Pearson Education, Inc.

2 , publishing as Pearson Prentice rights isometric drawing of a three-dimensional object shows An is the top view, front view, and right-side view of a three-dimensional net is DrawingMake an orthographic drawing of the isometric drawing at drawings flatten the depth of a figure. An orthographicdrawing shows views. Because no edge of the isometric drawing is hidden in the top, front,and right views, all lines are an orthographic drawing from this isometric ObjectivesMake isometric and orthographicdrawingsDraw nets for three-dimensionalfigures21 NAEP 2005 Strand:GeometryTopic:Dimension and ShapeLocal Standards: _____Lesson 1-2 Drawings, Nets, and Other Modelsa corner view of the figure drawnorthographic drawinga two-dimensional pattern you can fold to form a three-dimensional isometric dot Notetaking GuideGeometryLesson 1-1L1 Pearson Education, Inc.

3 , publishing as Pearson Prentice rights Class_____ Date Inductive ReasoningMake a conjecture about the sum of the cubes of the first 25 counting the first few sums. Notice that each sum is a perfect square and thatthe perfect squares form a sum of the first two cubes equals the square of the sum of the firstcounting numbers. The sum of the first three cubes equals thesquare of the sum of the first counting numbers. This patterncontinues for the fourth and fifth rows. So a conjecture might be that Quick a conjecture about the sum of the first 35 odd numbers. Use yourcalculator to verify your 3 11 1 1 131323 132333 13233343 1323334353225152100 102 36 62 9 32 1 1212 (1 2)2(1 2 3)2(1 2 3 4)2(1 2 3 4 5)22 Name_____ Class_____ Date _____threethe sum of the cubes of the first 25 counting numbers equals the square ofthe sum of the first 25 counting numbers, or (1 2 3.)

4 25)2. two12223242521491625 The sum of the first 35 odd numbers is 352, or Notetaking GuideGeometryLesson 1-2L1 Name_____ Class_____ Date a NetDraw a net for the figure with a square base and four isosceles triangle faces. Label the net with its 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 fourisosceles triangle faces is a side of the . Write in theknown drawing shows one possible net for the Graham Crackers a different net for this box. Show the dimensions in your diagram. GRAHAMCRACKERS GRAHAMCRACKERS14 cm14 cm7 cm20 cm20 cm7 cm10 cm8 cm2 Pearson Education, Inc., publishing as Pearson Prentice rights cm8 cmAnswers may vary. Example:14 cm7 cm20 cmAll-In-One Answers Version BGeometryL1 geometry : All-In-One Answers Version B(continued)GeometryLesson 1-3 Daily Notetaking GuideL16 Name_____ Class_____ Date_____ Pearson Education, Inc.

5 , publishing as Pearson Prentice rights and Key 1-1 Through any two points there is Line tis the only line that passes through points Aand .Postulate 1-2If two lines intersect, then they intersect in and intersect 1-3If two planes intersect, then they intersect in Plane RSTand plane STWintersect in .Postulate 1-4 Through any three noncollinear points there is A point isis the set of all line isare points that lie on the same line.*ST)SRTW*BD)*AE)ABDECABtLesson ObjectivesUnderstand basic terms of geometryUnderstand basic postulates ofgeometry21 NAEP 2005 Strand:GeometryTopic:Dimension and ShapeLocal Standards: _____Lesson 1-3 Points, Lines, and Planesexactly one one one series of points that extends in two opposite directions without pointsexactly one 1-4 Daily Notetaking GuideL18 Name_____ Class_____ Date_____ Pearson Education, Inc.

6 , publishing as Pearson Prentice rights segment isA is the part of a line consisting of one endpoint and all the points of the line on one side of the rays areare coplanar lines that do not lines areAB is to EF .AB and CG are planes that do not ABCD is to plane ObjectivesIdentify segments and raysRecognize parallel lines21 NAEP 2005 Strand:GeometryTopic:Relationships Among Geometric FiguresLocal Standards: _____Lesson 1-4 Segments, Rays, Parallel Lines and Planesthe part of a line consisting of tworaytwo collinear rays with the sameParallel linesnoncoplanar; therefore, they are not parallel and do not planesskewparallelparallelendpoints and all points between ABEndpointQR SXYRay YXEndpointABYX) are opposite )RQ)Endpoint7 Daily Notetaking GuideGeometryLesson 1-3L1 Name_____ Class_____ Date _____ Pearson Education, Inc.

7 , publishing as Pearson Prentice rights plane is Two points or lines are if they lie on the same postulate or axiom is Collinear PointsIn the figure at right,name three points that are collinear and three points that are not ,, and lie on a line, so they Postulate 1-4 Shade the plane that contains X,Y, and ,Y, and Zare the vertices of one of the four triangular faces of the pyramid. To shade the plane, shade the interior ofthe triangle formed by ,, and .Quick the figure in Example points W,Y, and Xcollinear? line min three different plane a point that is coplanar with points V,W, and ABCABCan accepted statement of flat surface that has no may vary. Sample: , , .*YZ)*WY)*ZW)Y9 Daily Notetaking GuideGeometryLesson 1-4L1 Name_____ Class_____ Date _____ Pearson Education, Inc.

8 , publishing as Pearson Prentice rights Segments and RaysName the segments and rays in the labeled points in the figure are A,B, and segment is a part of a line consisting of two endpoints and all pointsbetween them. A segment is named by its two endpoints. So thesegments are and .A 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, followedby any other point on the ray. So the rays are Parallel PlanesIdentify a pair of parallel planes in your are parallel if they. If the walls of your classroomare vertical,walls are parts of parallel planes. If the ceiling andfloor of the classroom are level, they are parts of parallel ThinkingUse the figure in Example form a line.

9 Arethey opposite rays? the diagram to the three pairs of parallel a line that is parallel to . a line that is parallel to plane QRUV.*PQ)SQPTUVWRBC)CB)2 ABC1BA (or AB)BC (or CB)BA)BC)do not intersectoppositeNo; they do not have the same RQVU, PRUT SQVW, PSQR TWVUA nswers may vary. Sample: *PS)*TV) Pearson Education, Inc., publishing as Pearson Prentice rights Answers Version BL12 geometry : All-In-One Answers Version B(continued) Pearson Education, Inc., publishing as Pearson Prentice rights 1-5 Daily Notetaking GuideL110 Name_____ Class_____ Date_____ Pearson Education, Inc., publishing as Pearson Prentice rights and Key 1-5: Ruler PostulateThe points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the Postulate 1-6: Segment Addition PostulateIf three points A,B, and Care collinear and Bis between Aand C, thenA coordinate isthe length of R Qacoordinate of Acoordinate of Bare segments with the same midpoint is AB2 cmCD2 cmCDAB AB CDuAB5uABabABABCL esson ObjectivesFind the lengths of segments1 NAEP 2005 Strand:MeasurementTopic:Measuring Physical AttributesLocal Standards.

10 _____Lesson 1-5 Measuring Segmentsabsolute value of the difference of theAB BC point s distance and direction from zero on a number ( ) segmentsa point that divides a segment into two || midpointBCABG eometryLesson 1-6 Daily Notetaking GuideL112 Pearson Education, Inc., publishing as Pearson Prentice rights Class_____ Date_____Vocabulary and Key 1-7: Protractor PostulateLet and be opposite rays in a plane.,, and all the rays with endpoint Othat can be drawn on one side ofcan be paired with the real numbers from 0 to 180 so paired with and is paired with . is paired with xand is paired with y,then .Postulate 1-8: Angle Addition PostulateOD)OC)OB)OA)*AB)OB)OA)OB)OA)Les son ObjectivesFind the measures of anglesIdentify special angle pairs21 NAEP 2005 Strand:MeasurementTopic:Measuring Physical AttributesLocal Standards: _____Lesson 1-6 Measuring AnglesmlCOD5ux2yuIf point Bis in the interior of AOC, thenm m m AOC.