Geometry Notes 7.1.notebook
C.P. Geometry
7.1 Ratios and Proportions
Objective: To write ratios and solve proportions.
A ___________ is a comparison of two quantities. You can write the ratio of two numbers a and b, where b ≠ 0, in three ways: a/b, a:b, and a to b. The two numbers should be written in the same unit and expressed in simplest form.
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An extended ratio compares three (or more) numbers. In the extended ratio a:b:c, the ratio of the first two numbers is a:b, the ratio of the last two numbers is b:c, and the ratio of the first and last numbers is a:c.
Example: The lengths of the sides of a triangle are in the extended ratio 4:7:9. The perimeter is 60 cm. What are the lengths of the sides?
Example: A bonsai tree is 18 in. wide and stands 2 ft. tall. What is the ratio of the width of the bonsai to its height?
An equation that states that two ratios are equal is called a ________________. The first and last numbers in a proportion are the extremes. The middle two numbers are the means.
Example: The measures of two supplementary angles are in the ratio 1:4. What are the measures of the angles?
Key Concept: Cross Products Property
In a proportion, the product of the extremes equals the product of the means.
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Examples: What is the solution of each proportion?
b. 15 = 3 a. 9 = a 2 14 m + 1 m
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Example: Solve each equivalent proportion.
a. If x/6 = y/7, then 6/x = ?
b. If x/6 = y/7, then x/y = ?
c. If x/6 = y/7, then ? = (y + 7)/7
Key Concept: Properties of Proportions
a, b, c, and d do not equal zero.
(1) Reciprocal Property: If a/b = c/d, then b/a = d/c.
(2) Switching Means Property:
If a/b = c/d, then a/c = b/d.
(3) Adding One Property: If a/b = c/d, then (a + b)/b = (c + d)/d.
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