Geometry Properties of Equality and Congruence
Distributive Property
a(b+c)=ab+ac
Reflexive Property
a=a
Transitive Property
if a=b and b=c,then a=c
Multiplication/Division Properties
if a=b,then a ∙c=b∙c
Addition/Subtraction Properties
if a=b,then a+c=b+c
Symmetric Property
if a=b,then b=a
corresponding angles
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Reflexive Property
(AB) ̅≅(AB) ̅
Reflexive Property
(RS) ̅≅(RS) ̅.
Reflexive Property
AB=AB
Transitive Property
If (AB) ̅≅(BC) ̅ and (BC) ̅≅(CE) ̅,then (AB) ̅≅(CE) ̅.
Transitive Property
If (AB) ̅≅(CD) ̅ and (CD) ̅≅(EF) ̅ then (AB) ̅≅(EF) ̅
Symmetric Property
If (AB) ̅≅(CD) ̅,then (CD) ̅≅(AB) ̅
Definition of Angle Bisector
If (BD) ̅ is a bisector of ∡ABC, then m∡ABD=m∡DBC
Symmetric Property
If (DE) ̅≅(GH) ̅,then (GH) ̅≅(DE) ̅.
Substitution Property
If AB + BC = EF + FG and AB + BC = AC, then EF + FG = AC.
Transitive Property
If AB=CD and CD=EF, then AB=EF.
Transitive Property
If AB=CD and CD=EF,then AB=EF
Multiplication/Division Property
If AB=CD, then 1/2 AB=1/2 CD.
Symmetric Property
If AB=CD,then CD=AB
Transitive Property
If AB=RS and RS=WY, then AB=WY.
Addition/Subtraction Property
If AB=RS and TU=WY, then AB+TU=RS+WY.
Segment Addition Postulate
If B is between A and C, then AB+BC=AC.
Definition of Midpoint
If B is the midpoint of (AC) ̅, then AB=BC
Segment Addition Postulate
If Q is between P and R, then PR = PQ + QR.
Angle Addition Postulate
If R is in the interior of ∡PQS, then: m∡PQR+m∡RQS=m∡PQS.
Symmetric Property
If a-b=r, then r=a-b.
Substitution Property
If a=b, then a may be replaced by b in any equation or expression.
Substitution Property
If m∡1+m∡2=110 and m∡2=m∡3, then m∡1+m∡3=110
Substitution Property
If m∡1=90 and m∡2=m∡1, then m∡2=90.
Transitive Property
If m∡1=m∡2 and m∡2=m∡3, then m∡1=m∡3.
Symmetric Property
If m∡1=m∡2 then m∡2=m∡1.
Addition/Subtraction Property
If x+3=17, then x=14.
Addition/Subtraction Property
If x-5=6, then x=11.
Multiplication/Division Property
If x=5, then 2x=10.
Vertical Angles Theorem (not a definition)
If ∠1 and ∠2 are vertical angles, then m∡1=m∡2
Definition of a Linear Pair
If ∡1 and ∡2 form a linear pair, then m∡1+m∡2=180
Definition of Supplementary
If ∡ABC and ∡DEF are supplementary, then m∡ABC+m∡DEF=180
Reflexive Property
QA=QA.
Reflexive Property
RS=RS.
