For another proof of the Pythagorean theorem, consider a right triangle ABC (with right angle at C) whose legs have length a and b and whose hypotenuse has length c. On the extension of side BC pick a point D such that BAD is a right angle. A ac b а D a? сь B b From the similarity of triangles ABC and DBA, show that AD = ac/b and DC = a²/b. (b) Prove that a² + b? = c² by relating the area of triangle ABD to the areas of triangles ABC and (а) ACD.

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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Can you do #16 and #17 

For another proof of the Pythagorean theorem,
consider a right triangle ABC (with right angle at C)
whose legs have length a and b and whose
hypotenuse has length c. On the extension of side
BC pick a point D such that BAD is a right angle.
A
ac
b
а
D
a?
сь
B
b
From the similarity of triangles ABC and DBA,
show that AD = ac/b and DC = a²/b.
(b) Prove that a² + b? = c² by relating the area of
triangle ABD to the areas of triangles ABC and
(а)
ACD.
Transcribed Image Text:For another proof of the Pythagorean theorem, consider a right triangle ABC (with right angle at C) whose legs have length a and b and whose hypotenuse has length c. On the extension of side BC pick a point D such that BAD is a right angle. A ac b а D a? сь B b From the similarity of triangles ABC and DBA, show that AD = ac/b and DC = a²/b. (b) Prove that a² + b? = c² by relating the area of triangle ABD to the areas of triangles ABC and (а) ACD.
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