1. 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.

2. 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. 3-4 Algebra Properties Used in Geometry Postulates of Equality For 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

4. 3-4 Algebra Properties Used in Geometry Postulates of Equality and Operation For 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

5. 3-4 Algebra Properties Used in Geometry Postulates of Inequality and Operation For 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 0, then ac < bc If a bc

6. 3-4 Algebra Properties Used in Geometry Postulates of Equality and Inequality For 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

7. 3-4 Algebra Properties Used in Geometry Distributive Property of Multiplication over Addition For any real numbers a, b and c: a(b + c) = ab + ac