Basic Proof of the Pythagorean Theorem:

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Presentation transcript:

Basic Proof of the Pythagorean Theorem: A=c2 A=a2 a c b A=b2

Use shapes to show: a2 ab a2 ab ab b2 b2 ab

Squaring a Binomial a2 b2 ab a b

Squaring a Binomial b a (b–a) a b b2 a (b–a)

Squaring a Binomial ab b2 ab a2 (b–a)2

Bhaskara’s Hindu Dissection Proof of the Pythagorean Theorem Can you re-arrange into a square with side c?

BEHOLD! The shortest known proof!

Bhaskara’s Hindu Dissection Proof of the Pythagorean Theorem (b–a) ? BEHOLD! c b a

Garfield’s Geometry or c a b Can you re-arrange these shapes into a trapezoid with bases a and b? c c

Garfield’s Geometry b a c

Homework Pythagorean Dissection Proof Pythagorean Word Problems

Name: Use the following diagram to show proof of the Pythagorean theorem.                               c a b