Download Multiplication‐ POSTULATE: If a and b are numbers such that a>b

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
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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
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Given: BA = 3BD
BC = 3BE
BE > BD
Prove: BC > BA
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Given: m ABC > m DEF
BG bisects ABC
EH bisects DEF
Prove: m ABG > m DEH
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Use an inequality postulate to prove the conclusion:
If 8 > 6, then 4 > 3
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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
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Two sides of a triangle have lengths 2 and 5. Find all possible lengths of the 3rd side.
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Homework:
5.3 pg 186 #1,4‐12,13,15
AND
5.4 pg 188 #1‐23odd
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