 Theorem - 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.

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Presentation transcript:

 Theorem - 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.

Let’s look at a right triangle… 5 cm 4 cm 3 cm

Each side has a certain length. What if we draw a square out from each side of the triangle? 5 cm 4 cm 3 cm

4 cm 3 cm 5 cm

4 cm 3 cm 5 cm

Now…think about the area of a square. How do we find it?

4 cm 3 cm 5 cm x 3 = 3 2 = 9

 After 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.  = 5 2  = 25

6 m 8 m ? A 2 + B 2 = C = ? = ? = ? 2 But remember, the missing side does not equal 100. It’s a number that equals 100 when it’s squared. ? = 10

5 ft 12 ft C A 2 + B 2 = C 2  = C 2  = 169 C 2 = 169, so C = √169 C = 13

15 in 9 in B When we are missing a leg rather than the hypotenuse, we must be sure to find either A or B in the equation. A 2 + B 2 = C 2  B 2 = 15 2  81 + B 2 = – 81 = 144  B 2 = 144  B = √144 = 12