# Pythagorean Theorem

Definition: Pythagorean Theorem describes the relationship between the three sides of a right triangle (remember… a right triangle must have a right angle!) It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Example: Find the hypotenuse of a right triangle with legs of measure 5cm and 12 cm.

Solution:

Step 1: Note that the theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse, that is, a² + b² = c².

Step 2: Substitute the value for the legs. (Note that each leg can either be a or b, e.i. either a = 5 and b = 12 or a = 12 and b = 5.) Using a = 5 and b = 12 we have 5² + 12² = c².

Step 3: Simplify ⇒ 25 + 144 = c² ⇒ 169 = c².

Step 4: Use reverse order of operations to solve for c ⇒ 169 = c² ⇒ √169 = √c² ⇒ 13 = c.

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