Introduction to Proofs

Algebraic Proofs Given each statement, match the property that justifies each statement. If 7x = 28, then x = 4. Division Property If y = 5x and 5x = 2z, then y = 2z. Transitive Property If a = b, then 2a = 2b Multiplication Property If a = b, then a - 9 = b - 9 Subtraction Property If 3x = 28 and 28 = 3x Symmetric Property If z = y , then z + 5 = y + 5. Addition Property Complete the following proof. Given: 8x – 5 = 2x + 1 Prove: x = 1 Statements Reasons 8x – 5 = 2x + 1 Given Statement 8x – 5 – 2x = 2x + 1 – 2x Subtraction Property 6x - 5 = 1 Substitution Property / Simplify 6x - 5 + 5 = 1 + 5 Addition Property 6x = 6 Substitution Property / Simplify 6 = 6 Division Property x = 1 Substitution Property / Simplify Complete the following proof. Angles 1 and 2 are complementary. Given The measure of angle 1 + the measure of angle 2 = 90 degrees Definition of complementary The measure of angle 2 is 74 degrees. Given The measure of angle 1 + 74 degrees = 90 degrees Substitution Property The measure of angle 1 is 16 degrees. Subtraction Property Complete the following proof. Angles 1 and 2 are supplementary. Given The measure of angle 1 + the measure of angle 2 = 180 degrees. Definition of Supplementary. The measure of angle 2 is 145 degrees. Given The measure of angle 1 + 145 degrees = 180 degrees. Substitution Property The measure of angle 1 = 35 degrees. Subtraction Property