3-4 Algebra Properties Used in Geometry

• The properties of operations of real numbers that you used in arithmetic and algebra can be applied in geometry.

3-4 Algebra Properties Used in Geometry

• There are three types of properties in mathematics:– Defining properties are those assigned to a

word in its definition.– Assumed properties are postulates.– Deduced properties are theorems.

3-4 Algebra Properties Used in Geometry

Postulates of EqualityFor any real numbers a, b and c:

– Reflexive Property of Equality:

a = a– Symmetric Property of Equality:

If a = b, then b = a– Transitive Property of Equality:

If a = b and b = c, then a = c

3-4 Algebra Properties Used in Geometry

Postulates of Equality and OperationFor any real numbers a, b and c:

– Addition Property of Equality:

If a = b, then a + c = b + c– Multiplication Property of Equality:

If a = b, then ac = bc

3-4 Algebra Properties Used in Geometry

Postulates of Inequality and OperationFor any real numbers a, b and c:

– Transitive Property of Inequality: If a < b and b < c, then a < c

– Addition Property of Inequality:If a < b, then a + c < b + c

– Multiplication Property of Inequality:If a < b and c > 0, then ac < bcIf a < b and c < 0, then ac > bc

3-4 Algebra Properties Used in Geometry

Postulates of Equality and InequalityFor any real numbers a, b and c:

– Equation to Inequality Property:

If a and b are two positive numbers and a + b = c, then c > a and c > b

– Substitution Property:

If a = b, then a may be substituted for b in any expression

3-4 Algebra Properties Used in Geometry

Distributive Property of Multiplication over AdditionFor any real numbers a, b and c:

a(b + c) = ab + ac