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