Algebraic Proof Addition:If a = b, then a + c = b + c. Subtraction:If a = b, then a - c = b - c. Multiplication: If a = b, then ca = cb. Division: If a = b, and c ≠ 0, then a  c = b  c

Algebraic Proof Substitution: If a + b = c and b = d, then a + d = c. Reflexive: a = a. Symmetric: If a = b, then b = a. Transitive: If a = b and b = c, then a = c. Distributive: a(b + c) = ab + ac.

Algebraic Proof Deductive Argument – A proof formed by a group of algebraic steps used to solve problems. Since geometry also uses variables, numbers, and operations, many of the properties of equality used in algebra are also true in geometry. (Examples: segment measures, angle measures)

Algebraic Proof Two-column proof (formal proof) – A form of deductive argument with statements and reasons organized in two-columns. Each step that advances the argument is called a statement. Each property, definition, rule, etc used to justify the statements are called reasons.

Example 6-1c Original equation Algebraic StepsProperties Distributive Property Substitution Property Subtraction Property Solve

Example 6-1d Substitution Property Division Property Substitution Property Answer:

Example 6-2f Write a two-column proof for the following. a.

Example 6-2g 1. Given 2. Multiplication Property 3. Substitution 4. Subtraction Property 5. Substitution 6. Division Property 7. Substitution Proof: Statements Reasons

Example 6-3d If and then which of the following is a valid conclusion? I. II. III. MULTIPLE- CHOICE TEST ITEM A I only B I and II C I and III D II and III Answer: C

Example 6-4b DRIVING A stop sign as shown below is a regular octagon. If the measure of angle A is 135 and angle A is congruent to angle G, prove that the measure of angle G is 135.

Example 6-4c Proof: StatementsReasons 1. Given 2. Given 3. Definition of congruent angles 4. Transitive Property