人教版新目标初中数学学习方法PEP new target junior high school mathematics learning method.docx

人教版新目标初中数学学习方法PEP new target junior high school mathematics learning method.docx

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人教版新目标初中数学学习方法PEPnewtargetjuniorhighschoolmathematicslearningmethod

人教版新目标初中数学学习方法（PEP,newtarget,juniorhighschoolmathematics,learningmethod）

Thereisonlyonestraightlineacrosstwopoints

2thelinebetweentwopointsistheshortest

3thesameangleorisometricequalmargin

4withtheangleofthecomplementofequalorconstant

5havingonlyonelineandperpendiculartotheknownline

6,thelineoutsideapointandthelineonallpointsconnectedbytheline,theverticallinesegmentistheshortest

7parallelaxiomsfollowapointoutsidethestraightlineandhaveonlyonelineinparallelwiththeline

8ifthetwolinesareparalleltothethirdlines,thetwolinesareparalleltoeachother

9correspondinganglesareequal,thetwoparallellines

10alternateanglesareequal,thetwoparallellines

11complementaryinterioranglesonthesameside,twoparallellines

12thetwoparallellines,correspondinganglesareequal

13twolineparallel,alternateanglesareequal

14thetwoparallellines,complementaryinterioranglesonthesameside

Thesumof15sidesofatriangleisgreaterthanthird

16inferthatthedifferencebetweenthesidesofatriangleislessthanthird

17triangletrianglesumtheoremthreeanglesandequalto180degrees

18inference1thetwoacuteanglesofrighttriangleoverlapeachother

19acorollaryofatriangleisequaltothe2cornersandtwoanglesitisadjacentand

20acorollaryofatrianglewith3cornersthananyoneanditisnotadjacent.

Thecorrespondingsidesof21congruenttrianglesandequalangles

22edgeaxioms（SAS）arecongruentwithtwotrianglesofequalanglesonbothsidesandtheirangles

23cornercorneraxiom（ASA）hastwotrianglescongruenthornsandtheiredgescorrespondingtotheequal

24inference（AAS）hadtwohornsandoneoftheangleonthesidecorrespondingtotheequaltwocongruenttriangles

25sideaxioms（SSS）havingtwoequaltrianglesequaltothreesides

26,bevelandrightsideaxioms（HL）havetwosidesofarighttrianglecorrespondingtothesamesideofarightangle

27theorem1thedistancebetweenpointsonthebisectorofanangletothesidesofthisangleisequal

Thepointatwhichthedistancebetween2and28anglesisthesameasinthebisectorofthisangle

Thebisectorof29anglesisthesetofallpointsequaltothetwosidesoftheangle

Twoand30areequalisoscelestriangletheoremofanisoscelestriangle（i.e.equalequilateralangle）

31inferthatthebisectorofthe1isoscelestrianglevertexisequaltothebaseandperpendiculartothebase

32thetopanglesoftheisoscelestriangle,thebisector,themiddlelineonthebottomedgeandtheheightonthebottomedgecoincidewitheachother

33corollary3equilateraltriangleswhoseanglesareequal,andeachangleequalto60degrees

34thedecisiontheoremofisoscelestriangle,ifatrianglehastwoanglesequal,thenthetwoanglesareequaltothesides（equalangles,equalsides）

35corollary1threeanglesareequaltriangleisanequilateraltriangle

36corollary2anisoscelestrianglewithanangleequalto60degreesisanequilateraltriangle

37inarighttriangle,ifanacuteangleisequalto30degrees,therightangleofitisequaltohalfoftheslope

38thecenterlineonthebevelofarighttriangleisequaltohalfofthebevel

Thepointatwhichthetwoendsofthelineofthelineofdivisionareequaltothe39endsoftheline

Apointequaltothedistancebetweentwoendpointsof40inversetheoremandalinesegment,intheverticalbisectoroftheline

Theverticalbisectorofa41linesegmentcanbeconsideredasasetofallpointsequaltothedistancebetweenpointsattheendofalinesegment

42theorem1thetwographsofastraightlinesymmetryarecongruentforms

43theorem2iftwographsaresymmetricalaboutastraightline,thenthesymmetryaxisistheverticalbisectorofthecorrespondingline

44theorems3.Twographsaresymmetricalaboutastraightline,iftheircorrespondinglineorextensionlineintersects,thentheintersectionpointisonthesymmetryaxis

The45inversetheoremisthatifthecorrespondingpointsofthetwographsareverticallydividedbythesameline,thenthetwofiguresaresymmetricalabouttheline

46Pythagoreantheoremofrighttriangletworightanglesidesa,bsquare,andthesquareisequaltothehypotenuseC,a^2+b^2=c^2

47thePythagoreantheoremandinversetheoremofa,ifthethreesideoftriangleB,Ca^2+b^2=c^2,thenthetriangleisarighttriangle

Intheorem48quadrilateralandequalto360degrees

49quadrilateralcornersandisequalto360degrees

Inthe50polygonsumtheoremnedgeshapeandisequalto（n-2）*180degrees

51anyinferencemultilateralangleandequalto360degrees

Thepropertytheoremof52parallelogram;thediagonalequalityof1parallelogram

Thepropertytheoremof53parallelogram;theequalsidesof2parallelogram

54parallelsbetweentwoparallellinesareequal

Thepropertytheoremof55parallelogram;diagonalbisectorof3parallelogram

56parallelogramdecisiontheorem1.Thetwogroupsofequalanglesareparallelogram

57parallelogramdecisiontheorem2.Thequadrilateraloftwosetsofequalsidesisparallelogram

The58parallelogramtheorem;3diagonalsequaltooneanother;thequadrilateralisaparallelogram

59theparallelogramtheorem4isaparallelogramofparallelpairsofedgesequaltoaparallelogram

Fouranglesof60rectangulartheorem1rectangleisright

61rectangularpropertytheorem2thediagonalofarectangleisequal

62rectangulardecisiontheorem1hasthreeanglesatrightangles,andaquadrilateralisarectangle

63rectangulardecisiontheorem2aparallelogramwithequaldiagonalsisarectangle

64diamondtheorem1thefoursidesofadiamondareequal

65diamondtheorem2thediagonalsofthediamondareperpendiculartoeachotherandeachdiagonallineisdividedintoasetofdiagonalangles

Halfofthe66diamondarea=diagonalproduct,namelyS=（a*b）/2

67diamonddecisiontheorem1quadrilateralisequaltofoursidesisdiamond

68diamonddecisiontheorem2thediagonalsareperpendiculartoeachotherandtheparallelogramisrhombic

The69squaretheoremfouranglesof1squareisarightangle.Thefoursidesareequal

70thesquaretheoremof2squaresequaltotwodiagonals,andperpendiculartoeachother,eachdiagonalisequaltoasetofdiagonal

The71theorem1,aboutthecentralsymmetryofthetwographsarecongruent

72theorem2onthecentralsymmetryofthetwofigures,thesymmetrypointsareconnectedthroughthecenterofsymmetry,andisdividedbythesymmetrycenter

The73inversetheorem,ifthecorrespondingpointsofthetwographsareconnectedbyacertainpoint,andbythisone

Thepointbisection,thenthetwographsaresymmetricaboutthispoint

74isoscelestrapezoidpropertytheoremtheisoscelestrapezoidisequaltotwoanglesatthesamebottom

75isoscelestrapeziumwithtwodiagonalsequal

76isoscelestrapezoidjudgmenttheorem,onthesamebottom,thetwoanglesequaltrapezoidisisoscelestrapezoid

77thetrapeziumwithequaldiagonalsisisoscelestrapezoid

Atheoremof78parallellines,ifasetofparallellinesiscutinastraightline

Equal,thenthelinesegmentsthatarecutonotherlinesareequal

79inference1,aftertheladder,themiddleofawaistandthebottomparallelline,willbeequaltotheotherwaist

80inference2thelinebetweenthemidpointofthetriangleandtheothersidemustbeequal

Thethreeside

81themedianlineofatriangleinwhichthemedianlineofatriangleisparalleltothethirdsideandequaltoit

Half

Themedianlinetheoremofthe82laddertheorem.Themedianlineoftheladderisparalleltothetwobaseandequaltothesumofthetwobases

HalfoftheL=（a+b）/2S=L*h

83

（1）thebasicnatureoftheratio,ifa:

b=c:

d,thenad=bc

Ifad=bc,thena:

b=c:

d

84

（2）,iftheratioofa/b=c/D,then（a+b）/b=（c+D）/D

85（3）geometricproperties,ifa/b=c/d=...=m/N（b+d+...+n=0）,then

（a+c+...+m）/（b+d+）...+n）=a/b

86parallellinesaredividedintolinesegments.Thecorrespondingtheoremisthatthreeparallellinescuttwostraightlines

Proportionaltolinesegments

87inferenceparalleltothetrianglesideoftheline,cuttheotherside（ortheextensionlineonbothsides）,thecorrespondinglinesegmentsproportional

The88theorem,ifastraightlinecutsthecorrespondinglineofthetwosidesofthetriangle（ortheextensionlineonbothsides）,thenthelineisparalleltothethirdsideofthetriangle

89paralleltoonesideofthetriangleandintersectingwiththeothersides,thethreesidesofthetriangleareproportionaltothethreesidesoftheoriginaltriangle

90theoremsparalleltoonesideofthetriangleintersecttheothersides（orextensionlinesonbothsides）,andthetriangleissimilartotheoriginaltriangle

91similartrianglestheorem1cornersequaltwotriangles（ASA）

92rightangledtrianglesaredividedbytheheightoftwosidesofabevel.Thetriangleissimilartotheoriginalone

93decisiontheorem2,thetwosidesareproportionaltoeachotherandtheanglesareequal,andthetwotrianglesaresimilar（SAS）

94decisiontheorem3,threesidescorrespondingproportional,twotrianglesimilarity（SSS）

The95theorem,iftherightsideofarighttriangleandtherightanglearethreerightangles

Thecornerofthecornerisproportionaltoarightangle,sothetworighttrianglesaresimilar

96propertytheorem1,theratioofthecorrespondingtriangle,theratioofthecorrespondinglineandthecorrespondingangleflat

Theratioofthelinetolineisequal