05/06/23 2-4: Using Proof in Algebra 1

2-4: Using Proof in 2-4: Using Proof in Algebra Algebra

Expectation: L3.3.1: Know the Expectation: L3.3.1: Know the basic structure for a proof of an basic structure for a proof of an

“if, then” statement.“if, then” statement.

05/06/23 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) 620D) 740 E) 1,240

05/06/23 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.

05/06/23 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.

05/06/23 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.

05/06/23 2-4: Using Proof in Algebra 6

Parts of a Proof1. 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.

05/06/23 2-4: Using Proof in Algebra 7

Prove: If x – 8 = 12, then x = 20

Given: x – 8 = 12Prove: x = 20Proof:1. x – 8 = 12 1. 2. x – 8 + 8 = 12 + 8 2. 3. x + 0 = 20 3. 4. x = 20 4.

05/06/23 2-4: Using Proof in Algebra 8

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 = 9B.x ≠ 9C.3(x + 9) = 54D.3(x + 9) ≠ 54E.If 3(x+9) = 54, then x=9.

05/06/23 2-4: Using Proof in Algebra 9

05/06/23 2-4: Using Proof in Algebra 10

Complete Study Guide/Practice 2-4.

05/06/23 2-4: Using Proof in Algebra 11

Assignment pages 96-97, # 13-21 (odd), 22, 23,

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