Modeling Pythagorean Theorem - Geometrically. Template.

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Presentation transcript:

Modeling Pythagorean Theorem - Geometrically

Template

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

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

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

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

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

Figure 1

Figure 2

So what did we Discover? B B C C A x A B x B A A Give our Legs & Hypotenuse Names: A, B & C

So what did we Discover? B B C C A x A B x B A A A 2 + B 2 = C 2 WHICH IS THE PYTHAGOREAN THEOREM