Geometry Section 9.2 The Pythagorean Theorem. In a right triangle the two sides that form the right angle are called the legs, while the side opposite.

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Presentation transcript:

Geometry Section 9.2 The Pythagorean Theorem

In a right triangle the two sides that form the right angle are called the legs, while the side opposite the right angle is called the hypotenuse.

The Pythagorean Theorem is one of the most useful theorems in all of mathematics. It is named for the Greek mathematician Pythagoras, who is believed to have written the first proof of the theorem. Through the years the Pythagorean Theorem has been proofed in many different ways and by many different people including the U.S. president James A. Garfield.

The Pythagorean Theorem For any right triangle with hypotenuse c and legs a and b, the sum of the squares of the legs ( )is equal to the square of the hypotenuse ( ).

A Pythagorean Triple is three whole numbers that could be the sides of a right triangle.

Example: If a 25-foot ladder is leaning against a house and the bottom of the ladder is 9 feet away from the house, how far up the side of the house is the top of the ladder? Round to the nearest 1000 th.

Example: A coyote wondering in the desert leaves his den and walks 6 miles due north. He turns right and travels 3 miles east. Finally, he turns north again and travels for 2 miles. To the nearest 1000 th of a mile, how far is the coyote from his den in a straight.