TextbookReference:Pages682‐693
PostulatesandTheorems‐Geometry
Page3
Topic4–CongruentTriangles
ThirdAnglesTheorem
Ifthetwoanglesofonetrianglearecongruenttotwoanglesof
anothertriangle,thenthethirdanglesarecongruent.
Side‐Side‐Side(SSS)Postulate
Ifthreesidesofonetrianglearecongruenttothreesidesof
anothertriangle,thenthe
twotrianglesarecongruent.
Side‐Angle‐Side(SAS)Postulate
Iftwosidesandtheincludedangleofonetriangleare
congruenttotwosidesandtheincludedangleofanother
triangle,thenthetwotrianglesarecongruent.
Angle‐Side‐Angle(ASA)Postulate
Iftwoanglesandtheincludedsideofonetriangleare
congruentto
twoanglesandtheincludedsideofanother
triangle,thenthetwotrianglesarecongruent.
Angle‐Angle‐Side(AAS)Theorem
Iftwoanglesandanon‐includedsideofonetriangleare
congruenttotwoanglesandanon‐includedsideofanother
triangle,thenthetwotrianglesarecongruent.
IsoscelesTriangleTheorem
Ifwosidesofatrianglearecongruent,thentheanglesopposite
those
sidesarecongruent.
Corollary
Ifatriangleisequilateral,thenthetriangleisalso
equiangular.
Theorem4‐5
Ifalinebisectsthevertexangleofanisoscelestriangle,then
thelineisalsotheperpendicularbisectorofthebase.
Hypotenuse‐Leg(HL)Theorem
Ifthehypotenuseandalegofonerighttrianglearecongruent
tothehypotenuseandalegofanotherrighttriangle,
thenthe
trianglesarecongruent.
Topic6–PolygonsandQuadrilaterals
PolygonAngle‐SumTheorem
Thesumofthemeasuresofann‐gonis
2180n
Corollary
Themeasureofeachangleofaregularn‐gonis
2 180n
n
PolygonExteriorAngle‐SumTheorem
Thesumofthemeasuresoftheexterioranglesofapolygon,
oneateachvertex,is360.
Topic6cont’d–PropertiesofParallelograms
ParallelogramOppsides
Ifaquadrilateralisaparallelogram,thenitsoppositesidesare
congruent.
Oppsides
Parallelogram
Ifbothpairsofoppositesidesofaquadrilateralarecongruent,
thenitisaparallelogram
ParallelogramConsec.AnglesareSupp.
Ifaquadrilateralisaparallelogram,thenitsconsecutiveangles
aresupplementary.
Consec.AnglesareSupp Parallelogram
Ifallpairsofconsecutiveanglesinaquadrilateralare
supplementary,thenitisaparallelogram.
ParallelogramOpp.Anglesare
Ifaquadrilateralisaparallelogram,thenitsoppositeanglesare
congruent.
Opp.Angles
Parallelogram
Ifbothpairsofoppositeanglesofaquadrilateralare
congruent,thenitisaparallelogram.
ParallelogramDiags.bisecteachother
Ifaquadrilateralisaparallelogram,thenitsdiagonalsbisect
eachother.
Diags.Bisecteachother Parallelogram
Ifbothdiagonalsofaquadrilateralbisecteachother,thenitis
aparallelogram.
Anglesupp.tobothconsecanglesParallelogram
Ifanangleofaquadrilateralissupplementarytobothofits
consecutiveangles,thenthequadrilateralisaparallelogram.
Onepairoppsides
and||Parallelogram
Ifonepairofoppositesidesofaquadrilateralisbothcongruent
andparallel,thenitisaparallelogram.
Rhombus diagonals
Ifaparallelogramisarhombus,thenitsdiagonalsare
perpendicular.
diagonalsRhombus
Ifaquadrilateralisaparallelogramwithperpendicular
diagonals,thenitisarhombus.