2/26/20162-4: Using Proof in Algebra1 Expectation: L3.3.1: Know the basic structure for a proof of an “if, then” statement.

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Presentation transcript:

2/26/ : Using Proof in Algebra1 Expectation: L3.3.1: Know the basic structure for a proof of an “if, then” statement.

2/26/ : Using Proof in Algebra2 A rectangular lot measures 125 feet by 185 feet is completely fenced. What is the approximate length, in feet, of the fence? A) 310B) 435C) 620 D) 740E) 1,240

2/26/ : Using Proof in Algebra3 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.

2/26/ : Using Proof in Algebra4 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.

2/26/ : Using Proof in Algebra5 Algebraic Properties of Equality Distributive Property: For all real numbers a, b and c, a(b + c) = ab + ac.

2/26/ : Using Proof in Algebra6 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.

2/26/ : Using Proof in Algebra7 Prove: If x – 8 = 12, then x = 20 Given: x – 8 = 12 Prove: x = 20 Proof: 1. x – 8 = x – = x + 0 = x = 204.

2/26/ : Using Proof in Algebra8 Prove: If 3(x-4) = 36, then x = 16.

In a proof of the conditional statement, “If 3(x + 9) = 54, then x = 9,” what should be accepted ad true? A.x = 9 B.x ≠ 9 C.3(x + 9) = 54 D.3(x + 9) ≠ 54 E.If 3(x+9) = 54, then x=9. 2/26/ : Using Proof in Algebra9

2/26/ : Using Proof in Algebra10 Complete Study Guide/Practice 2-4.

2/26/ : Using Proof in Algebra11 Assignment pages 96-97, # (odd), 22, 23, 24