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The Pythagorean Theorem

Activity Description Activity GuideResources

Students create both a visual and formal proof of the Pythagorean theorem, as well as view four additional geometric demonstrations of the theorem. These demonstrations are based on proofs by Bhaskara, Leonardo da Vinci, and Euclid. Students will value this activity more if they have already had some experience with the Pythagorean Theorem.

Mathematics: The students will construct a square and conjecture the following theorem:

  • The sum of the areas of the squares on the legs of a right triangle is equal to the area of the square on the hypotenuse.

The extension activity includes investigating the converse of the Pythagorean theorem, and generalizing the theorem to shapes other than squares.

Mathematical Thinking: Students will be asked to conjecture, prove and generalize the aforementioned theorem.

Technology: The students will use several Sketchpad features such as: Scripts, Text tool, Area, Polygon Interior, and Sample Sketches.

The following sketch illustrates a visual demonstration of the Pythagorean Theorem.

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Last modified on August 13, 2001.