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2-4: Using Proof in Algebra

2-4: Using Proof in Algebra . Expectation: L3.3.1: Know the basic structure for a proof of an “if, then” statement. A rectangular lot measures 125 feet by 185 feet is completely fenced. What is the approximate length, in feet, of the fence? A) 310 B) 435 C) 620 D) 740 E) 1,240.

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2-4: Using Proof in Algebra

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  1. 2-4: Using Proof in Algebra Expectation: L3.3.1: Know the basic structure for a proof of an “if, then” statement. 2-4: Using Proof in Algebra

  2. A rectangular lot measures 125 feet by 185 feet is completely fenced. What is the approximate length, in feet, of the fence? • A) 310 B) 435 C) 620 D) 740 E) 1,240 2-4: Using Proof in Algebra

  3. Equivalence Properties of Equality • Reflexive Property of Equality: • For all real numbers a, a = a. • Symmetric Property of Equality: • For all real numbers a and b, if a = b, then b = a. • Transitive Property of Equality: • For all real numbers a, b and c, if a = b and b = c, then a = c. 2-4: Using Proof in Algebra

  4. Algebraic Properties of Equality • Addition Property of Equality: For all real numbers a, b and c, if a = b, then a + c = b + c. • Multiplication Property of Equality: For all real numbers a, b and c, if a = b, then ac = bc. • Substitution Property of Equality: If a=b, then you may replace a with b in any equation containing a. 2-4: Using Proof in Algebra

  5. Algebraic Properties of Equality • Distributive Property: For all real numbers a, b and c, a(b + c) = ab + ac. 2-4: Using Proof in Algebra

  6. Parts of a Proof • 1. Given: the hypothesis of the conditional. • Assume this to be true. • 2. Prove: the conclusion of the conditional. • 3. The proof: a logical chain of statements starting with the given and ending with the prove. Each statement must be justified with a mathematical statement. 2-4: Using Proof in Algebra

  7. Prove: If x – 8 = 12, then x = 20 • Given: x – 8 = 12 • Prove: x = 20 • Proof: • 1. x – 8 = 12 1. • 2. x – 8 + 8 = 12 + 8 2. • 3. x + 0 = 20 3. • 4. x = 20 4. 2-4: Using Proof in Algebra

  8. Prove: If 3(x-4) = 36, then x = 16. 2-4: Using Proof in Algebra

  9. In a proof of the conditional statement, “If 3(x + 9) = 54, then x = 9,” what should be accepted ad true? • x = 9 • x ≠ 9 • 3(x + 9) = 54 • 3(x + 9) ≠ 54 • If 3(x+9) = 54, then x=9. 2-4: Using Proof in Algebra

  10. Complete Study Guide/Practice 2-4. 2-4: Using Proof in Algebra

  11. Assignment • pages 96-97, # 13-21 (odd), 22, 23, 24 2-4: Using Proof in Algebra

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