Pythagoras Without Squares

Strategies and Hints

  1. In the isosceles right triangles, each area equals half the square of the side. Divide both sides of the pythagorean relationship by 2 to prove the extension for this figure.

  1. In these triangles, each area equals one-fourth the square of the side. Students should divide by 4 to prove the extension.

  2. For equilateral triangles, multiply each term of the Pythagorean theorem by

Solution

Multiply by and divide by 8 to prove the extension for semicircles.

 

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