Unit 1: Introduction To Geometry Notes Day 6 Algebraic Proofs Worksheet With Answers

Geometry Support Unit 1—Introduction to Geometry Notes Name_____________________________ Date__________________ Day 6—Algebraic Proofs 1. Solve the following equation. 2. Rewrite your proof so it is “formal” proof. Justify each step as you solve it. 2(4x - 3) – 8 = 4 + 2x 2(4x - 3) – 8 = 4 + 2x Proof: An argument that uses logic, definitions, properties, and previously proven statements to show a conclusion is true Postulate: Statement that are accepted as true without proof. Theorem: Statement that can be proven true. Two Column Proofs • ______________________________________________ • ______________________________________________ • ______________________________________________ Geometry Support Unit 1—Introduction to Geometry Notes Name of Property Statement of Property Example Student Version M o s t H e lp fu l Addition Property of Equality If a = b, then a + c = b + c I can add the same thing to both sides of an equation without changing the solutions. Subtraction Property of Equality If a = b, then a – c = b – c I can subtract the same thing from both sides of an equation without changing the solutions. Multiplication Property of Equality If a = b, then ac = bc I can multiply both sides of an equation by the same number (other than 0) without changing the solutions. Division Property of Equality If a = b and c  0, then a / c = b / c I can divide both sides of an equation by the same number (other than 0) without changing the solutions. Distributive Property of Equality For any real numbers a, b, and c: a (b + c) = ab + ac I can distribute a number outside parentheses to each term inside parentheses without changing the meaning of the expression. Simplify (Combine Like Terms) For any real numbers a, b, and x: ax + bx = (a + b)x I can combine like terms without changing the eaning of the expression. Symmetric Property of Equality If a = b, then b = a I can swap the sides of an equation without changing the solutions. H e lp fu l in G e o m e tr y Reflexive Property of Equality For any real number a: a = a Any number is equal to itself. Transitive Property of Equality If a = b and b = c, then a = c If I’m the same as Chris and Chris is the same as Pat, then I’m the same as Pat. Substitution Property of Equality If a = b, then a can be substituted for b in any expression or equation If I know the value of a variable, I can substitute that into other expressions and equations. Geometry Support Unit 1—Introduction to Geometry Notes Fill in the blanks to finish the proofs. 1. Given: 5 18 3 2x x− = + Prove: 10x = 2. Given: 2 6 8 3 x − = Prove: 15x = 3. Given: 4(5 7) 3 12 27x x x+ − = − Prove: 11x = − Statements Reasons 1. 1. Given 2. 5 3 20x x= + 2. 3. 3. Subtraction Property 4. 4. Division Property Statements Reasons 1. 1. 2. 2. Multiplication Property 3. 2 30x = 3. Addition Property 4. 15x = 4. Statements Reasons 1. 4(5 7) 3 12 27x x x+ − = − 1. 2. 20 28 3 12 27x x x+ − = − 2. 3. 3. Combine like terms 4. 4. Subtraction Property 5. 5. Subtraction Property 6. 11x = − 6. Geometry Support Unit 1—Introduction to Geometry Notes 4. Given: 6x – 4 = 3x + 8. Prove: x = 4 Statement Reason 5. Given: 48 = 5(2x – 7) + 3. Prove: x = 8 Statement Reason 6. Solve 5 2 8 x + = . Prove: x = 11 Statement Reason STATEMENTS REASONS Geometry Support Unit 1—Introduction to Geometry Notes 7. Given: 11 3( 4) 2x= − + Prove: 7x = 8. Given: 2(3 6) 4 2x x− − = + Prove: 1x = 9. Given: 2 6 12 4 x + = Prove: 21x =