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.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

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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