高二数学棱柱与棱锥二b版High school mathematicsprism and pyramid two b EditionWord下载.docx

高二数学棱柱与棱锥二b版High school mathematicsprism and pyramid two b EditionWord下载.docx

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Thepropertiesof2pyramidofknowledge

（1）high,andslantonthebottomsurfaceoftheslantpyramidprojectiveformatrianglepyramid;

highlateralandlateralribsonthebottomsurfaceoftheprojectiveformarighttriangle;

thesideedgeandthebottomedgeofofbendingpyramid,（partof）arighttriangleinthebottomofthepyramid;

slantprojectioninthesideedgeandthebottom,thebottomsurfaceoftheprojection（part）toformarighttriangle.（Figure9-9-55:

RtVDH,RtVAH,RtVAD,DeltaDeltaDeltaRtHAD）calculation.Thatisofteninthepyramidabovefourrightangledtriangle,isespeciallyimportant.

（2）usingafrustumofaplaneparalleltothebaseplane,thecrosssectionissimilartothebase,andsomeofthesidesareproportional,andtheareaisproportionaltothesquareofthecorrespondingedge

（3）itisespeciallypyramid,eachsideedgeisequal,eachsidearecongruentisoscelestriangle

SpecialknowledgeinSection3Pyramid:

diagonalplane（sectiontwoisnotadjacenttothesideedgeareparalleltothebottomsurfaceofthesection）.

Sideareaformulaof4pyramidofknowledgepoint

Thedrawingofhorizontalhorizontaldrawingof5straightpyramidofknowledgepoint:

obliquetwomeasuringmethod"

Relativeconceptsandpropertiesofknowledgepoints,6polyhedraandregularpolyhedra

Especiallyregularpolyhedron,ithasandonlyfivekinds（namely,regulartetrahedron,regularhexahedron,positiveeightbody,positivetwelvebody,positivetwentybody）

Knowledgepoint7usesthepropertiesofpyramidstostudytherelationbetweenthelinesandlines,linesandplanes,planesandplanes,andcalculatesthedistances,thethreeanglesandtheareaandvolumeofthepyramids

Problemsolvingmethodsandskillstraining

Theproofandcalculationoftherelationbetweenthelineandthelineinthe1pyramid

Figure9956in1cases,fourpyramidPABCD,bottomABCDisarightangledtrapezoid,angleBAD=90degrees,AD=BC,AB=BC=a,AD=2A,PA,ABCDandPDfacethebottomsurface,thebottomsurfaceatanangleof30degrees.

（1）iftheAEgroupPD,Egroup:

BEPDpedal,confirmation;

（2）thedifferentsurfacelinesAEandCDintothecorner.

[analysis]carefulanalysisisnotdifficulttofindgraphicfeatures,PA,BAandDA22areperpendiculartoeachother,whichistheestablishmentofthecoordinatesystem,toprovidetheconditionsofsolidgeometryproblemistransformedintoavector,inordertofindtheeasywaytogiveyouone.

[proof]

（1）takeAastheorigin,andAB,ADandAPtakethelineasthecoordinateaxis,andestablishtheCartesiancoordinatesystem

PDgroupofABandR,tAEPDdreams,

PDBE.*t

（2）dreamsofanomalousPAsurfaceABCD,PDandthebottomsurfaceatanangleof30degrees,

L/PDA=30~E,EFtAD,AEpedalF=A/EAF=60deg,

I

（1）insolvingtheproblemwithvector,tochoosethecoordinatesystem,findoutthecoordinatesofthepoint,writethevectorcoordinates.

（2）insolvingtheproblemsconcernedwithpyramid,shouldmakefulluseofthedefinitionandcharacterofthepyramid,andifthepyramidonthesurfaceofthepoint,line,spacetendtofigure"

"

theproblemofplane.

Theproofandcalculationoftherelationbetweenthelineandthesurfaceinthe2pyramid

2casesofknown:

fourPABCDpyramid,thebottomsurfaceisarightangledtrapezoid,whichAB,CD,BAtAD,PADtsidebottomABCD,

（1）:

confirmationofanomalousPCDplanePADplane;

（2）ifAB=2,CD=4,PBCisequaltothepositivesideofthelongsideofthetriangle10theACandPCDforthediagonalsideanglesinevalue.

（1）[analysis]itisprovedthattheplaneandtheplanearevertical.Generally,thejudgmenttheoremofthelineandthesurfaceisvertical

[prove]dreamsquadrilateralABCDrightangledtrapezoid,"

CD.ABsaid

AndthedreamsofanomalousPADbottomABCDsurface,abottomsurfacePADABCD=AD,

ADgroupAB,ABgroupofPAD.star

（2）[analysis]weshouldgrasptheprojection"

angle"

for"

lineandplaneangle"

[solution]by

（1）,PADgroupandPADPCD,aplanesurfacePCD=PD.*PADinthesurfaceinAAHgroupPD.H.AHgroupofpedalPCD（theoremverticalsurface）.ThenconnecttoCH,thenACHforfrontline,facetheangles（Figure9-9-61）.

Ilineandplaneangle"

graspingprojective.

Determinetheprojectivepointsdependson"

nature"

theoremofverticalsurface.The"

verticalline"

and"

surfacevertical"

isoftenuseeachotherandtransformintoeachother.

Theproofandcalculationoftherelationbetweentheplaneandthesurfaceinthe3pyramid

3casesinfigure9966,ABCDABtBCDtetrahedron,plane,BC=CD/BCD=90/ADB=30degrees,Edegrees,F,AC,ADrespectivelyisthemidpoint.

（1）:

confirmationofanomalousBEFplaneABCplane;

（2）calculatetheangleofplaneBEFandplaneBCD

[analysis]toprovethatthetwoplanesarevertical,thatis,toproveaplanethroughanotherplaneofaverticalline,soyouneedtoproveastraightlineandtheplaneoftheintersectionoftwoverticallines,andtoprovethatthetwoverticalline,

（1）[]thatestablishedinFigure9-9-67showsthespacecoordinatesystem,A（0,0,a）,a/ADB=30deg,

Iusevectorcoordinatecalculationinthree-dimensionalgeometry,playeda"

countgenerationcard"

effect,reducethedegreeofdifficulty,embodiesthenewoutlineofthespirit.

Thecalculationoftheareaandvolumeinthe4pyramid

4casesofknownplaneanomalousADEplaneABCD,DeltaADEisthesidelengthofaABCDisanequilateraltriangle,rectangle,FisthemidpointofAB,ECandABCDplaneatanangleof30degrees,

（1）forthefourEAFCDpyramidvolume;

（2）E-CF-Dforthedihedralanglesize（;

3）fortheDEFCpointtosurfacedistance.

（1）[solution]inFigure9-9-72,EADgroupofABCDdreams,andEADisanequilateraltriangle,triangularEprojectivepointonthebottomoftheABCDonH,ADandADinthemidpointofthelinkHC/ECH,then=30degrees.

（2）[analysis]forE-CF-Ddihedralangle,bydefinitionof"

law"

（i.e."

threeverticaltheorem"

astheangle,angle）,youcanalsousethe"

projectiveareamethod"

.

StardeltaHFCisarightangledtriangle.AndtheanomalousHF/EFHasdefinedbyFC.thattheplaneEFCDdihedralangle,inRtDeltaEFH,

I"

volumeconversionmethod"

isacommonlyusedmethodofpointtoplanedistance.Itsideaissimple,easytomaster.

Easilymixedwarning

Intheunderstandingofthedefinitionofpyramidattentionmustbepaidtotheconditionsinthedefinition:

"

therestofthesurfaceisacommonvertexofthetriangle"

.Somegeometricpropertiesofthepyramidistobestraightenedout,clear,alsoshouldbepaidattentiontoandlateralside,thebottomofthepyramidlocation.

5caseshavethefollowingpropositionofthebottomsurfaceispolygonalpyramidisorthoprism;

allsideedgelengthequalisthepyramidisapyramidpyramid;

canhavetwosideedgesperpendiculartothebottomsurface;

andapyramidcanhavetwosidesperpendiculartothebottomsurface,wherein,thecorrectproposition（）

A.0B.1

C.2D.3

[means]chooseAorCorD.

[analysis]wrongduetothecauseoftheerroristheconceptandnatureofthepyramidisnotclearenoughonthelineandline,lineandsurface,surfaceandsurfaceproperties,themasteryandapplicationoftheoremisnotinplace,infact,aslongasthedefinitionofthepropositionarefamiliarpyramidwillnotgowrong,thepyramidprismsinthesamelengthofpropositionatthebottom,canonlydeterminethevertexprojectivepoint,butnotsureitispositiveifthepyramidpyramid,propositiontwosideedgeisperpendiculartothebottomsurface,thetwosideedgewillbeparallel,thenitisnotapyramid,thepropositionofapyramidcanhavetwosidesperpendiculartothebottomsurface,aslongasapyramidsideedgeisperpendiculartothebottomsurface,itwillhavetwosidesandperpendiculartothebottomsurface,soright.

[]a.B.positivesolution

Integratedapplicationinnovation

[integratedcapabilitiesupgrading]

Thepyramidasacarrier,acomprehensivetestoftherelationshipbetweenthepositionoflineandplaneproblemisanotherkeyprobleminsolidgeometry.Tosolvetheseproblems,acorrectunderstandingofavarietyofdifferentpositionsinthepyramidlines;

twotomastertheanalysisandsolvecommonproblemsinsolidgeometry.

6casesinFigure9-9-75,P-ABCDinthefourpyramid,anomalousPBbottomABCD.CDtPD,ABCDbottomisarighttrapezoid,AD"

BCAB,anBC,AB=AD=PB=3,EPAandPEintheedge,=2EA.

（1）thedifferentsurfacelinesPAandCDintothecorner;

（2）:

PC//EBDplaneconfirmation;

（3）forthesizeofABEDdihedralangle;

（1）[analysis]accordingtotheconceptoftheangleofthedifferentstraightline,inthebottomoftheABCD,theAcanfind