*GeometricBasics

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

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

Collinear PointsLie on the same line. (The line does not have to be visible).

*ABCABCCollinearNon collinear

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

Different planes in a figure:

*ABCDEFGHPlane ABCDPlane EFGHPlane BCGF Plane ADHEPlane ABFEPlane CDHGEtc.

Other planes in the same figure:Any three non collinear points determine a plane!*Plane AFGDPlane ACGEPlane ACHPlane AGFPlane BDGEtc.

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

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.

Congruent SegmentsDefinition:Congruent segments can be marked with dashes.Segments with equal lengths. (congruent symbol: )

Ray*Definition:How to sketch:How to name:

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.

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.

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.*

Intersection of Two Planes is a Line.*PRABPlane P and Plane R intersect at the line

*Segment BisectorsAny segment, line or plane that divides a segment into two congruent parts is called segment bisector.Definition:

Between*Definition: X is between A and B if AX + XB = AB.AX + XB = ABAX + XB > AB

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

You Try It!

Complete Practice Problemsand check your answers withone another.

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