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Proving Pythagoras

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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 Step Two We ... – PowerPoint PPT presentation

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Title: Proving Pythagoras


1
Proving Pythagoras
  • By Marshall Knauf
  • Bhaskaras 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/bb/c
  • Multiply both sides by b/c
  • xcb2

a
b
h
B
x
y
C
M
c
6
Step 5
  • Angle CAB Angle AMC
  • y/a a/c
  • Multiply both sides by ac
  • yc a2

A
a
b
h
B
x
y
C
M
c
7
Step 6
A
  • Add results
  • ycxc a2b2
  • c(xy) a2b2
  • c2 a2b2
  • 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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