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Pythagorean Theorem

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Pythagorean Theorem

Pythagorean TheoremTheorem - A general proposition not self-evident but proved by a chain of reasoning.

In math a theorem is an idea that can be proven true by logical explanation. What?

Homer knows it, sort of. Okay, from Homer we learned that it only works for what kind of triangle?

Right trianglesLets look at a right triangle5 cm4 cm3 cmEach side has a certain length. What if we draw a square out from each side of the triangle?Lets draw some squares.5 cm4 cm3 cmNow, lets split each square into single cm blocks.4 cm3 cm5 cmSomething interesting happens when we count up the number of blocks in each square4 cm3 cm5 cm91625The number of blocks in the two smaller squares add up to the number of blocks in the larger square. Nowthink about the area of a square. How do we find it?

The number of blocks is the area of the square, or the length of the side squared4 cm3 cm5 cm333 x 3 = 32 = 9After all that, the Pythagorean Theorem comes down to this simple equation.

The length of each side squared must equal the length of the longest side (hypotenuse) squared.

32 + 42 = 52 9 + 16 = 25A2 + B2 = C2We can now use this to find the length of a side on a right triangle as long as we know the other two sides. 6 m8 m?A2 + B2 = C262 + 82 = ?236 + 64 = ?2100 = ?2But remember, the missing side does not equal Its a numberthat equals 100when its squared.? = 105 ft12 ftCA2 + B2 = C2 52 + 122 = C2 25 + 144 = 169C2 = 169, so C = 169C = 1315 in9 inBWhen we are missing a leg rather than the hypotenuse,we must be sure to find either A or B in the equation.A2 + B2 = C2 92 + B2 = 152 81 + B2 = 225225 81 = 144 B2 = 144 B = 144 = 12


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