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Modeling Pythagorean Theorem - Geometrically

Modeling Pythagorean Theorem - Geometrically. 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

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Modeling Pythagorean Theorem - Geometrically

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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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