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Proving Pythagoras

Proving Pythagoras. By Marshall Knauf Bhaskara’s Second Proof of the Pythagorean Theorem. Step One. Start with a right triangle Legs= a, b Hypotenuse= c. c. a. b. Step Two. A. We label the triangle with lines a, b, and c Points A, B, and C Lines x, y Altitude h. a. b. h. B. x.

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Proving Pythagoras

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  1. Proving Pythagoras By Marshall Knauf Bhaskara’s Second Proof of the Pythagorean Theorem

  2. Step One • Start with a right triangle • Legs= a, b • Hypotenuse= c c a b

  3. Step Two A • We label the triangle with lines a, b, and c • Points A, B, and C • Lines x, y • Altitude h a b h B x y C M c

  4. Step Three A • Proof by similar triangles • ABM~ CAB • ACM~ CAB • Angle Angle similarity a b h B x y C M c

  5. Step 4 A • Angle B = Angle BAM • x/b=b/c • Multiply both sides by b/c • xc=b^2 a b h B x y C M c

  6. Step 5 A • Angle CAB = Angle AMC • y/a = a/c • Multiply both sides by ac • yc = a^2 a b h B x y C M c

  7. Step 6 A • Add results • yc+xc = a^2+b^2 • c(x+y) = a^2+b^2 • c^2 = a^2+b^2 • Thus, Pythagoras is proven a b h B x y C M c

  8. Credits Everything Marshall Knauf Thank You www.jwilson.coe.uga.edu for the proof

  9. One More Thing May 5th Vote Marshall Knauf ASB Activities Commissioner

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