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Pythagorean Theorem: Geometric Modeling and Discoveries

Explore Pythagoras' mathematical discoveries and model the theorem visually. Understand the relationship between legs and hypotenuse of right triangles geometrically. Exercise with cutting and rearranging triangles to discover A2 + B2 = C2.

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Pythagorean Theorem: Geometric Modeling and Discoveries

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  1. Modeling Pythagorean Theorem - Geometrically

  2. Pythagoras • Born in Greece (Isle of Samos) • Around 570 B.C. • Settled in Italy • Credited with the following mathematical discoveries: • The Sum of Angles in Polygons • Irrational Numbers ( 2 ) • Five Regular (Platonic) Solids • Pythagorean Theorem

  3. Modeling Pythagorean Theorem • First, Understand Squaring Units Geometrically • If I have 5 Blocks like so… • Squaring those would look like this 5 5

  4. Modeling Pythagorean Theorem • Applied to the Legs of Right Triangles • It looks like this…

  5. Modeling Pythagorean Theorem • What is the Relationship between the Legs Squared • …and the Hypotenuse Squared?

  6. Exercise • Cut the Triangles Out Like So… • And piece them back together in Square adjacent to the Hypotenuse.

  7. Figure 1

  8. Figure 1

  9. Figure 1

  10. Figure 2

  11. Figure 2

  12. Figure 2

  13. So what did we Discover? Give our Legs & Hypotenuse Names: A, B & C A x A B x B A x A B x B A2 B2 C2 A C A2 B2 C2 A C B B

  14. So what did we Discover? A2 + B2 = C2 A x A B x B A x A B x B A2 B2 C2 A C A2 B2 C2 A C B B WHICH IS THE PYTHAGOREAN THEOREM

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