Geometric Basics
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Transcript of Geometric Basics
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*GeometricBasics
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PointsPoints do not have actual size.
How to Sketch: Using dots
How to label:
Use capital letters
Never name two points with the same letter in the same sketch. *ABA
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LinesExtend indefinitely and have no thickness or width.How to sketch : using arrows at both ends.
How to name: 2 ways(1) small script letterline n(2) any two points on the line
Never name a line using three points *nABC
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Collinear PointsLie on the same line. (The line does not have to be visible).
*ABCABCCollinearNon collinear
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PlanesFlat surface that extends indefinitely in all directions. How to sketch: Use a parallelogram (four sided figure)How to name: 2 ways(1) Capital script letter Plane M(2) Any 3 non collinear points in the planePlane: ABC/ ACB / BAC / BCA / CAB / CBA*ABCHorizontal PlaneMVertical PlaneOther
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Different planes in a figure:
*ABCDEFGHPlane ABCDPlane EFGHPlane BCGF Plane ADHEPlane ABFEPlane CDHGEtc.
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Other planes in the same figure:Any three non collinear points determine a plane!*Plane AFGDPlane ACGEPlane ACHPlane AGFPlane BDGEtc.
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Coplanar ObjectsCoplanar objects (points, lines, etc.) lie on the same plane. The plane does not have to be visible.*Are the following points coplanar?A, B, C ?A, B, C, F ?H, G, F, E ?E, H, C, B ?A, G, F ?C, B, F, H ?YesNoYesYesYesNo
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Segment*Part of a line that consists of two points called the endpoints and all points between them.How to sketch:How to name:Definition:AB (without a symbol) means the length of the segment or the distance between points A and B.
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Congruent SegmentsDefinition:Congruent segments can be marked with dashes.Segments with equal lengths. (congruent symbol: )
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Ray*Definition:How to sketch:How to name:
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Opposite Rays*Definition:( Opposite rays must have the same endpoint )opposite raysnot opposite raysIf A is between X and Y, AX and AY are opposite rays.
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Intersection of FiguresThe intersection of two figures is the set of points that are common in both figures.*The intersection of two lines is a point.mnPLine m and line n intersect at point P.
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3 Possibilities of Intersection of aLine and a Plane
(1) Line passes through plane intersection is a point.(2) Line lies on the plane - intersection is a line.(3) Line is parallel to the plane - no common points.*
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Intersection of Two Planes is a Line.*PRABPlane P and Plane R intersect at the line
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*Segment BisectorsAny segment, line or plane that divides a segment into two congruent parts is called segment bisector.Definition:
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Between*Definition: X is between A and B if AX + XB = AB.AX + XB = ABAX + XB > AB
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The Segment Addition PostulateIf C is between A and B, then AC + CB = AB.Postulate:Example:If AC = x , CB = 2x and AB = 12, then, find x, AC and CB.2xx x = 4AC = 4CB = 8Step 1: Draw a figureStep 2: Label fig. with given info.Step 3: Write an equationStep 4: Solve and find all the answers
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You Try It!
Complete Practice Problemsand check your answers withone another.
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