CK12 - Geometry

If two pointsare in a plane,then the wholeline throughthosetwo pointsis in the

plane.

Postulate 3

Postulate 4 If two distinctlines intersect,then the intersectionis exactlyone point.

Comments:Somelinesintersect,somedo not. If linesdo intersect,it is in only one

point,otherwiseone or both “lines”wouldhaveto curve,whichlines do not do.

Postulate 5 If two distinctplanesintersect,then the intersectionis exactlyone line.

Comments:Someplanesintersect,somedo not. Thinkof a floor and a ceilingas

modelsfor planesthat donotintersect.If planesdo intersect,it is in a line. Thinkof

the edgeof a box (a line) formedwheretwo sidesof the box (planes)meet.

The RulerPostulate: The pointson a line can be assignedreal numbers,so that for

any two points,one correspondsto 0 and the othercorrespondsto a nonzeroreal

Postulate 6

number.

Comments:This is how a numberline and a rulerwork.This also meanswe can

measureany segment.

The SegmentAdditionPostulate: Points and are collinearif and only if

.

Postulate 7

Comment:If and are not collinear, then .We saw

examplesof this fact in earliersectionsof this chapter.

The ProtractorPostulate: If rays in a planehavea commonendpoint, can be

assignedto one ray and a numberbetween and can be assignedto eachof

Postulate 8

the otherrays.

Comment:This meansthat any anglehas a (degree)measure.

The AngleAdditionPostulate: Let and be pointsin a plane. is in

the interiorof if and only if + =.

Postulate 9

Comment:If an angleis madeup of otherangles,the measuresof the component

anglescan be addedto get the measureof the “big” angle.

Postulate 10 The MidpointPostulate: Everyline segmenthas exactlyone midpoint.

Comments:If is a pointon and thereis not anotherpointon

,let’s say point ,with .The midpointof a segmentisunique.

Postulate 11 The AngleBisectorPostulate: Everyanglehas exactlyone bisector.