Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

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Garfield’s Proof

Transcript of Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Page 1: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Garfield’s Proof

Page 2: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

of theGarfield’s Proof

Page 3: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Pie- thagorean Theorem

Garfield’s Proofof the

Page 4: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Garfield’s Proofof the

Pie- thagorean Theorem

Page 5: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Garfield’s Proofof the

Pie- thagorean Theorem

Page 6: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Garfield’s Proofof the

Pie- thagorean Theorem

Pie-

Page 7: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Garfield’s Proofof the

Pie- thagorean Theorem

Py

Page 8: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Garfield’s Proofof the

Py

thagorean Theorem

(President)

Page 9: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Garfield’s Proofof the

Py

thagorean Theorem

(President)

Page 10: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

See Garfield eat Pie A

Garfield The Cat’s Proof

Page 11: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

President Garfield’s Proof:

Examine these three triangles.

a

b

a

b

c

c

c

c

Their area is

2

2

1c

ab2

1

ab2

1

abab2

1

2

1ab 2

2

1c

Page 12: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

See Garfield eat Pie A

See Garfieldeat Pie B

Page 13: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

a b

ab

c

c

The President’s great idea was to constructa trapezoid using these three triangles. yx bbhA

2

1

The area formula for a trapezoid is:

22 22

12

1

baba

babaA

In this case, we get:

Page 14: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

See me squared!

This isDr. Mena’sclass, so we’ve got

One Dead Cat

x x

Page 15: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

Then President Garfield noticed something astonishing!!

22 22

1baba 2

2

1cab abab

22

2

12 ba

2

2

12 c

22 ba 2c

Page 16: Garfield’s Proof of the Garfield’s Proof Pie- thagorean Theorem Garfield’s Proof of the.

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