1-3 Points, Lines, and Planes1-3點(diǎn)線與planesppt課件

1、Chapter 1: Tools of Geometry1- 3 Points, Lines, and PlanesObjectives, student will be able: 41. To understand basic terms of geometry.42. To understand basic postulates of geometry.4CW/HW: pgs. 19-21 #s 2 48 Even PointsHow to sketch:How to label:Macintosh PICTim age form atis not supportedMacintosh

2、PICTim age form atis not supportedMacintosh PICTim age form atis not supported* Use capital printed letters.* dotsABCA* Never label two points with the same name (in the same sketch). *Think of points as location markers. *Points are zero dimensional.Collinear PointsCollinear points are points that

3、lie on the same line. (The line does nothave to be visible.)M a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dnon-collinearcollinearM a c in to s h P IC Tim

4、 a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dDefinition: LinesHow to sketch:How to label:1- small “script” letter* must have arrows at both ends2- any two points on the line(T

5、wo methods)M a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dM a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dnM acintosh PIC Tim age form atis not supportedM acintosh P IC Tim age form atis not supportedM

6、 acintosh P IC Tim age form atis not supportedM acintosh P IC Tim age form atis not supportedM acintosh P IC Tim age form atis not supportedM acintosh P IC Tim age form atis not supportedMacintosh PICTimage formatis not supportedPossible Names:?PlanesHow to sketch:How to label:* horizontal* vertical

7、1- capital “script” letter2- any three points on the plane(Two methods)M a c i n t o s h P I C Ti ma g e f o r ma ti s n o t s u p p o r t e dM a c in t o s h P IC Tim a g e f o r m a tis n o t s u p p o r t e d* otherhorizontal “edges”vertical “edges”MPNMacintosh PICTimage formatis not supportedThi

8、nk of a plane as a flat surface that has no thicknessA plane contains an infinite many lines and extends without endPlanesHow to label: #2- any three points on the planePlanesHow to label: any three points on the planeMacintosh PICTimage formatis not supportedHow many planes do you see?PlanesHow to

9、label: any three (or more) points on the planeMacintosh PICTimage formatis not supportedHow many planes do you see?M a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dplane ABCDplane ABCplane BCDplane CDAplane DABetc.PlanesHow to label: any three (or more) points on the planeMacintosh

10、PICTimage formatis not supportedHow many planes do you see?plane EFGHplane EFGplane FGHplane GHEplane HEFetc.M a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dPlanesHow to label: any three (or more) points on the planeMacintosh PICTimage formatis not supportedHow many planes do you s

11、ee?plane AEHDplane EHDplane HDAplane DAEplane AEHetc.M a c in t o s h P IC Tim a g e f o r m a tis n o t s u p p o r t e dPlanesHow to label: any three (or more) points on the planeMacintosh PICTimage formatis not supportedHow many planes do you see?plane BFGCplane BFGplane FGCplane GCBplane CBFetc.

12、M a c in t o s h P IC Tim a g e f o r m a tis n o t s u p p o r t e dPlanesHow to label: any three (or more) points on the planeMacintosh PICTimage formatis not supportedHow many planes do you see?plane ABFEplane ABFplane BFEplane FEAplane EABetc.Macintosh PICTimage formatis not supportedPlanesHow t

13、o label: any three (or more) points on the planeMacintosh PICTimage formatis not supportedHow many planes do you see?plane DCGHplane DCGplane CGHplane GHDplane HDCetc.Macintosh PICTimage formatis not supportedPlanesHow to label: any three (or more) points on the planeMacintosh PICTimage formatis not

14、 supportedAny three points determine a plane!plane AGFplane BDGetc.plane AFGDMacintosh PICTimage formatis not supportedplane ACGEM a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dplane ACHM a c in to s h P IC Tim a g e fo rm a tis n o t s u p p o rte dCoplanarCoplanar objects (points

15、 or lines) are objects that lie on the same plane. (The plane does not have to be visible.)Definition: Macintosh PICTimage formatis not supportedAre they coplanar?ABC ?yesABCF ?NOHGFE ?yesEHCB ?yesAGF ?yesCBFH ?NOPostulate or Axiom4A postulate or axiom is an accepted statement as fact.4Postulate and

16、 Axioms have no formal proof they exist or are true4Many mathematicians do years of research trying to prove postulates or axioms true.4Postulates and axioms that are proven true are known as Theorems.Postulate 1-14Through any two points there is exactly one line.4Line t is the only line that passes

17、 through points A and B.M a c in to s h P IC Tim a g e fo r m a tis n o t s u p p o r te dPostulate 1-24If two lines intersect they intersect in exactly one point4 and intersect at C. Macintosh PICTimage formatis not supportedMacintosh PICTimage formatis not supportedMacintosh PICTimage formatis not supportedPostulate 1-34If two planes intersect, then they intersect in exactly one line.4Plane RST and4Plane STW4Intersect in4 .M acintosh PICTim age form atis not supportedM acintosh PICTim age form atis not supportedM acintosh PICTim age form atis not supportedPostulate 1-44Through any three