# Pythagorean Theorem Proofs

There are more than 50 ways to prove the Pythagorean theorem. Using the Library, web resources, and other course materials, choose a proof of the theorem that you understand and describe it to the class. Then create a real-world application problem that can be solved by using the Pythagorean theorem. Make sure to include the question, calculations, and the solution.

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#### Solution Preview

(a) Proof of Pythagoras Theorem by the Area Method:

Statement: In a right triangle, the square on the longest side (hypotenuse) is equal to the sum of the squares on the other two sides.

Given: A right triangle ABC, with hypotenuse length c and the other two legs measuring a ...

#### Solution Summary

One of the many ways of proving the Pythagorean Theorem is presented. Also included is a real-world application problem.

Problems with Quadratic Reciprocity & Pythagorean Triangles

2. If p>3, show that p divides the sum of its quadratic residues that are also least residues.

(see attached file for diagram)

4. Here is a quadrilateral, not a parallelogram, with integer sides and integer area:

(a) What is its area?

(b) Such quadrilaterals are not common; can you find another?

(c) Could you find 1,000,000 more?