Geometry Properties of Equality and Congruence

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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

...

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.


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