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Geometry 6-1
Big Idea: Use Ratios & Proportions
Ratio A comparison of two A comparison of two numbersnumbersEx.1) ½, 1:2
Ex.2) 3 , 3:4 4
Example 7 weeks: 14 days(convert to the same units in order
to compare, then simplify) Method 1: 49 days = 7 (reduce) 14 days 2 Method 2: 7 weeks = 7 2 weeks 2
Proportions
An equation that states that 2 ratios An equation that states that 2 ratios are equal.are equal.
1 = 2 (Read as:
2 4 “1 is to 2 as 2 is to 4”)
1 = 2
2 4
extremes & means(extremes are the first and last terms)
(means are the middle terms)
Property of Cross Products of a Proportion:
the product of the means always equals the product of the extremes
Ex.1) 1 = 2
2 4 (1·4 = 2·2)
Ex.2) 3 = 6_ (3·14 = 7·6)
7 14
Example: Solve the proportion
Example: solve the proportion
Example: Find the dimensions (l, w) of a wall whose perimeter is 484 m and whose ratio of length to width is 9:2.
An extended ratio compares more than 2 numbers.
Example: The measures of the angles of a triangle are in the extended ratio of 3:4:8. Find the angle measures.
The geometric mean is the positive number, if placed in the position of the means makes the proportion a true statement.
The geometric mean of 2 positive numbers (a & b) is “x” where
a = x x b Then by the rule of cross-products,
x(x) = ab and x2 = ab
√x2 = √ab x = √ab
Example: Find the geometric mean of 32 & 8.
Example: Find the geometric mean of 16 & 18.