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Multiplication‐ POSTULATE: If a and b are numbers such that a>b and c is a positive number, then ac > bc IN WORDS: If ≠ quantities are multiplied by = positive quantities, the products are ≠ in the same order Ex) If 9>7 and 4=4, then 9(4) > 7(4) or 36 > 28 Ex) If AB > DE, AC=2AB and DF=2DE, then AC > DF ‐‐‐‐> because doubles of unequal quantities are unequal in the same order 1 Division‐ POSTULATE: If a and b are numbers such that a>b and c is a positive number, then a > b c c IN WORDS: If ≠ quantities are divideded by = positive quantities, the quotients are ≠ in the same order Ex) If 12>8 and 4=4, then 12/4 > 8/4 or 3 > 2 Ex) If AC < AB, AE=(1/2)(AC), and AD = (1/2)(AB) then AE < AD ‐‐‐‐‐> because halves of unequal quantities are unequal in the same order 2 Given: BA = 3BD BC = 3BE BE > BD Prove: BC > BA 3 Given: m ABC > m DEF BG bisects ABC EH bisects DEF Prove: m ABG > m DEH 4 Use an inequality postulate to prove the conclusion: If 8 > 6, then 4 > 3 5 Ch 5.4: Side Lengths of a Triangle Theorem: The sum of the lengths of 2 sides of a triangle is greater than the length of the 3rd side ‐‐‐> we only need to add the 2 shorter sides to see whether their sum is greater than the 3rd ‐‐‐> Which of the following may be the lengths of the sides of a triangle? (1) 2,3,5 (2) 4,4,8 (3) 3,4,8 (4) 5,6,7 6 Two sides of a triangle have lengths 2 and 5. Find all possible lengths of the 3rd side. 7 Homework: 5.3 pg 186 #1,4‐12,13,15 AND 5.4 pg 188 #1‐23odd 8