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Pythagorean Theorem Proof Unit 4 Project Grace Olson.

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Presentation on theme: "Pythagorean Theorem Proof Unit 4 Project Grace Olson."— Presentation transcript:

1 Pythagorean Theorem Proof Unit 4 Project Grace Olson

2 Four equal Right Triangles a a a a b bb b c c c c

3 Find the area of the Large Square a b a b c a b c a b c c Find the area of the large square: The area of a square = a side squared The side is = a + b The are of the square = (a + b) = (a + b)(a + b) = a + 2ab + b 2 22

4 Find the area of a Triangle a b a b c a b c a b c c The area of the Triangles = ½ ab

5 Find the area of Four Triangles a b a b c a b c a b c c The area of the four triangles = 4(½ ab) = 2ab 1 2 3 4

6 Find the area of the Small Square a b a b c a b c a b c c The area of the Small Square = c 2

7 Restate the area of the Large Square a b a b c a b c a b c c The area of the Large Square = the area of the Small Square + the area of the Four Triangles The area of the Small Square = c + The area of the Four Triangles = 4(½ ab) = 2ab c + 2ab 2 1 2 3 4 2 2

8 Set the areas equal a b a b c a b c a b c c c + 2ab = a + 2ab + b Simplify c + 2ab = a + 2ab + b c = a + b 1 2 3 4 2 2 2 2 2 2 22 2

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