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Proving Pythagoras

- By Marshall Knauf
- Bhaskaras 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

y

C

M

c

Step Three

A

- Proof by similar triangles
- ABM CAB
- ACM CAB
- Angle Angle similarity

a

b

h

B

x

y

C

M

c

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

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

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

Credits

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

One More Thing

- May 5th
- Vote Marshall Knauf
- ASB Activities Commissioner

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