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A standard proof of the Pythagorean theorem starts with a right triangle ABC, with its right angles at C, and then draws a perpendicular CD from C to the hypotenuse AB. C a D C b B (a) Prove that triangles ACD and CBD are both similar to triangle ABC. (b) For a triangle ABC with legs of lengths a and b and with hypotenuse of length c, use the proportionality of corresponding sides of similar triangles to establish that a? + b² = c².

A standard proof of the Pythagorean theorem starts with a right triangle ABC, with its right angles at C, and then draws a perpendicular CD from C to the hypotenuse AB. C a D C b B (a) Prove that triangles ACD and CBD are both similar to triangle ABC. (b) For a triangle ABC with legs of lengths a and b and with hypotenuse of length c, use the proportionality of corresponding sides of similar triangles to establish that a? + b² = c².

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A standard proof of the Pythagorean theorem starts with a right triangle ABC, with its right angles at C, and then draws a perpendicular CD from C to the hypotenuse AB. C a D C b B (a) Prove that triangles ACD and CBD are both similar to triangle ABC. (b) For a triangle ABC with legs of lengths a and b and with hypotenuse of length c, use the proportionality of corresponding sides of similar triangles to establish that a? + b² = c².
Transcribed Image Text:A standard proof of the Pythagorean theorem starts with a right triangle ABC, with its right angles at C, and then draws a perpendicular CD from C to the hypotenuse AB. C a D C b B (a) Prove that triangles ACD and CBD are both similar to triangle ABC. (b) For a triangle ABC with legs of lengths a and b and with hypotenuse of length c, use the proportionality of corresponding sides of similar triangles to establish that a? + b² = c².
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