If a=b, then a-c=b-c Vertical Angle Congruence Theorem Distributive Property Substitution Property of Equality Subtraction Property of Equality

Subtraction Property of Equality

If a=b, then ac=bc Transitive Property of Equality Multiplication Property of Equality Addition Property of Equality Distributive Property

Multiplication Property of Equality

a=a Reflexive Property of Equality (reflection) Right Angle Congruence Theorem Subtraction Property of Equality Multiplication Property of Equality

Reflexive Property of Equality (reflection)

If a=b, then b can be substituted for a in any expression Addition Property of Equality Substitution Property of Equality Transitive Property of Equality Multiplication Property of Equality

Substitution Property of Equality

If a=b and b=c, then a=c Transitive Property of Congruence Transitive Property of Equality Distributive Property Linear Pair Postulate

Transitive Property of Equality

If AB ≅ CD and CD ≅ EF, then AB ≅ EF. Addition Property of Equality Symmetric Property of Equality Multiplication Property of Equality Transitive Property of Congruence

Transitive Property of Congruence

For all vectors u and v in R^n, u + v is in R^n. The sum of two vectors in R^n is always a vector in R^n Distributive law two scalars Distributive law one scalar Scalar distribution The Set of all R^n is CLOSED UNDER VECTOR ADDITION

The Set of all R^n is CLOSED UNDER VECTOR ADDITION

There is a zero vector 0 in R^n such that 0+u = u for all vectors u in R^n. In fact, 0 = (0, 0, ....., 0). The Set R^n is CLOSED UNDER SCALAR MULTIPLICATION Distributive law one scalar R^n contains an ADDITIVE IDENTITY ELEMENT Each vector u in R^n contains a MULTIPLICATIVE IDENTITY ELEMBENT 1

R^n contains an ADDITIVE IDENTITY ELEMENT

For each vector u in R^n, there is a unique vector u in R^n such that u + (u) = 0. In fact, if u = (u1, u2, . . . , un) then -u = (-u1, -u2, . . . , -un) Distributive law one scalar Vector Addition is ASSOCIATIVE Each vector in R^n has a unique ADDITIVE INVERSE in R^n Distributive law two scalars

Each vector in R^n has a unique ADDITIVE INVERSE in R^n

For all scalars c in R and all vectors u in R^n, cu is a vector in R^n R^n contains an ADDITIVE IDENTITY ELEMENT The Set R^n is CLOSED UNDER SCALAR MULTIPLICATION Vector Addition is ASSOCIATIVE The Set of all R^n is CLOSED UNDER VECTOR ADDITION

The Set R^n is CLOSED UNDER SCALAR MULTIPLICATION

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