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

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.3: The Rectangle, Square, And Rhombus

Problem 42E: a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three...

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