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Unformatted text preview: The Basic Proportionality Theorem Initial Results: A B C H D CH = 2.93 inches All triangles with a common base and common altitude have EQUAL AREAS . AB = 6.60 inches Area ABD = 9.65 inches 2 Area ABC = 9.65 inches 2 1 2 AB CH = 9.65 inches 2 Common base = Common altitude = D E F G A C B H FG = 1.65 inches When two triangles have a common altitude, the RATIO of their AREAS equals the RATIO of their BASES. Area DEF = 0.96 inches 2 Area ABC = 3.84 inches 2 AB = 4.66 inches DE = 1.17 inches CH = 1.65 inches RED Data BLUE Data RATIOS: Area ABC) ( Area DEF) ( = 4.00 AB DE = 4.00 Proof of (1) [ Proving BD / DA = BE / EC ]: The following pairs of triangles are triangles with equal height: The pair DAE and BDE, and the pair ECD and BED , and the pair AEC and ADC; The Basic Proportionality Theorem Let ABC be a given triangle. Suppose that D and E are points on sides BA and BC, resp., such that DE || AC ....
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This note was uploaded on 11/02/2010 for the course MATH modern geo taught by Professor Shirley during the Spring '10 term at University of Texas.
- Spring '10