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Unformatted text preview: 12-1 Similarity
A) The Idea of a Similarity; Proportion a. Similarity i. Figures have the same shape but not necessarily the same size ii. Examples b. Proportional i. Given two sequences a, b, c, ... and p, q, r, ... of positive numbers. If then the sequences a, b, c, ...and p,q,r,... are called proportional, and we write a,b,c,...~ p,q,r,...
ii. The symbol ~ is pronounced "is proportional to" iii. example 2,3,4 ~ 4,6,8 This works because B) Theorem 12-1 a. Proportionality between sequences is an equivalence relation i. What are the three things that have to hold for an equivalence relation? C) Variations of basic proportions a.
b. Cross multiply, we get i. Divide on both sides bq, we get i. Adding 1 to both sides, we get c. d. e. i. Subtracting 1 to both sides, we get i. D) Geometric Mean
a. If a, b, and c are positive numbers and , then b is called the geometric mean between a and c. i. What will b equal? E) Examples
a. b. c. If 2a = 7, then d. Find the geometric mean a. 1 and 4 b. 12 and 15 ...
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- Spring '09