几何定理总归纳（geometric theorem, general induction）

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1、几何定理总归纳（Geometrictheorem,generalinduction）1pointsandonlyastraightline2theshortestlinebetweentwopoints3thesameangleorisometricequalmargin4withtheangleofthecomplementofequalorconstant5alittlebitandonlyastraightlineandtheverticallineisknownThe6lineapointandthestraightlineconnectingallthe

2、pointsontheline,verticallineistheshortest7parallellinesthroughapointoutsidetheaxiom,andonlyastraightlinewiththeparallelline8ifthetwolineandthirdlineparalleltothetwolinesareparalleltoeachother9correspondinganglesareequal,thetwoparallellines10alternateanglesareequal,thetwoparallellines1

3、1complementaryinterioranglesonthesameside,twoparallellines12thetwoparallellines,correspondinganglesareequal13twolineparallel,alternateanglesareequal14thetwoparallellines,complementaryinterioranglesonthesameside15theoremsonbothsidesofthetriangleisgreaterthanthethirdsideThe16sidesofthet

4、rianglethatislessthanthirdedges17triangletrianglesumtheoremthreeanglesandequalto180degrees18corollarytwoacute1righttrianglesarecomplementary19acorollaryofatriangleisequaltothe2cornersandtwoanglesitisadjacentand20acorollaryofatrianglewith3cornersthananyoneanditisnotadjacent.Thecorrespo

5、nding21congruenttriangleedge,correspondingangle.The22corneredgeaxiom(SAS)therearetwocongruenttrianglesonbothsidesandtheircorrespondingequalangle23cornercorneraxiom(ASA)hastwotrianglescongruenthornsandtheiredgescorrespondingtotheequal24inference(AAS)hadtwohornsandoneoftheangleontheside

6、correspondingtotheequaltwocongruenttrianglesThe25sideedgeaxiom(SSS)hastwotrianglescongruentthreesidescorrespondingtotheequal26hypotenuse,rightanglesideaxiom(HL)isthehypotenuseandarightanglesidecorrespondingtotheequaltwocongruentrighttriangles27theorem1inthebisectorofanglepointtoadista

7、nceequaltotheangleonbothsidesBothsidesofthe28theorem2toacornerofthedistancefromthesamepointinthebisectorofangleBisectorofangle29isthesetofallpointstobothsidesoftheangleofequaldistanceTwoand30areequalisoscelestriangletheoremofanisoscelestriangle(i.e.equalequilateralangle)31corollary1is

8、oscel