运用几何变换的特征创造性解题（the characteristics of creative problem solving using geometric transform）

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1、运用几何变换的特征创造性解题（Thecharacteristicsofcreativeproblemsolvingusinggeometrictransform）WorthhavingdataIsfromtheusualaccumulationoflearningsummaryTherearecertainlysomelocalproblemsAlsopleasecriticism!ThecharacteristicsofcreativeproblemsolvingusinggeometrictransformJiangsuProvince,TaizhouCit

2、y,KowloonexperimentalschoolGuGuanglin(225312)Geometrictransformationinjuniorhighschoolmathematicsgenerallyreferstotranslation,symmetry(fold)androtation."Mathematicscurriculumstandards"inthecurriculumgoalhasclearlypointedoutthat"theprocessoftransformation,basicnature,positiontoexplore

3、therelationshipbetweenobjectsandfigures"WeknowTheshapeandsizeofthegraphtransformationdoesnotchangethegraphicsOnlychangethegraphicspositionThecharacteristicsofproblemsolvingcanmakefulluseofgraphicstransformationThegraphicspositionchangeInordertooptimizethegraphstructureFurtherintegrat

4、ionofgraphics(problem)informationpurposesThecomplexproblemcanbecreativelysolved.Figure1casesDeltaABCADisthecenterlineDE,DF/ADB/ADCandwereequallyAB,AC,F.inEtoverify:BE+CF>EF.Asolutionof(symmetric)asshowninFigure1BytheknownconditionsThedeltaBDE,DeltaCDFrespectivelybyDE,DFaxisoffoldDelt

5、aMDE,DeltaMDFtransformEasyME=BEMF=CFThesethreelinesintoatriangleTheproblemsmoothlydoneoreasilysolved.Methodtwo(rotation)asshowninFigure2ThedeltaFDC180degreerotationaroundthepointDtransformintodeltaPDBPD=DFLinkPEByDEandDFastheanglebisectorTheEDgroupofPFThusEP=EFThisthreelineistransfor

6、medtodeltaBPEThepropositionofCertifcate.Methodthree(translation)asshowninFigure2BBP"CFFDlineinPEasyBPD=DeltaDeltaCFDThisCF=BPSotheconversionofthreelinestodeltaBPEthroughtranslationThepropositionofCertifcate.Comment:geometrictransformisapowerfultoolforproving.Thatlineismainlythroughth

7、eunequalrelationshipbetweentherelationshipbetweenthethreesidesofatriangle,whenthelinetothescatteredNotusingtherelationshipbetweenthethreesidesofatriangle.AccordingtothepropertiesoftheinvolvedinthegraphicsTothe(orpartthereof)asageometrictransformationSomeproblemsinrelationtoashiftinth

8、etriangleThi