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Unformatted text preview: 71 Geometric Inequalities
A) Inequalities for Numbers, Segments and Angles a. Definition i. If AB D CD , then
AB D CD ii. Or 1. One segment is less than or shorter than another if its length is less b. Definition i. If m D Am D B , then ii. Or A B 1. One angle is less than or shorter than another if its measure is less B) A review of some properties and a theorem a. Trichotomy Property (also called the Comparison Property) i. For every x and y only one of the following holds x y 1. x y x= y b. Transitive property i. If x D y and y D z , then x Dz c. Addition Property i. If a D b and x y , then a + x b+ y d. Multiplication Property i. If x D y and a 0 , then ax D ay e. Theorem 22 i. If a = b + c and c 0 , then a b C) Theorem 71 (The Parts Theorem) 1) If D is a point on AB between A and B, then AB AD and AB DB
2) If D is a point in the interior of
ABC DBC
D ABC , then ABC ABD and "The whole is greater than any one of its parts" ...
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This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State University.
 Spring '09
 Johnson
 Algebra

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