Harvard Extension Math for Teaching Capstone Project

2. Definition of Pythagorean Theorem

Pythagorean Theorem
In a right angled triangle the square of the long side, the hypotenuse or "c" is equal to the sum of the squares of the other two sides, "a" and "b". It is stated in this formula:

a² + b² = c²

3. Video tutor on the Pythagorean Theorem...

The Pythagorean Theorem has a converse, it is reversible, which means that a triangle whose sides satisfy a² + b² = c² is necessarily right angled. Euclid was the first (First book, Proposition 48) to mention and prove this fact. (http://www.cut-the-knot.org/pythagoras/)

4. Video tutor on its converse...

5. Math Crazy Tutor...

6. Pythagorean Side Finder

7. Proofs of Pythagorean Theorem

Shang Gao / Bhaskara
Shang Gao or Bhaskara Theorem

In this proof, the square on the hypotenuse plus four copies of the triangle can be assembled into the same shape as the squares on the other two sides plus four copies of the triangle. Four triangles of area 1/2ab are rearranged into two rectangles of area ab: proof by area manipulation. The first recorded use is in China (where it is alternately known as the "Shang Gao Theorem", named after the Duke of Zhou's astrologer, and described in the mathematical collection Zhou Bi Suan Jing) and in India, where it is known as the Bhaskara Theorem.(http://en.wikipedia.org/wiki/Pythagorean_theorem)

8. Proof by Rearrangement

9. Another proof by area manipulation.
Watch the animation and then try it yourself...

10. Now, try it yourself...

11. There are MANY more proofs of the Pythagorean Theorem. You can find more here and here.

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