Lesson 1: Pythagorean Theorem - Formula

   Constructing Knowledge

You have studied the Pythagorean Theorem in your previous math courses. You just did a geometric proof of the theorem in the Getting Into It activity.

Definitions needed for the Pythagorean Theorem:




Right triangle
any triangle that contains a right angle (90° angle)

Legs
the two sides of the triangle that make up the 90° angle

Hypotenuse (hi·pot·e·nuse)
the side of the triangle across from the right angle. It is always the longest side of a right triangle.

Notice that the right angle symbol in the corner of the triangle 'points' to the hypotenuse regardless of the triangle's orientation.

Formula


The Pythagorean Theorem states that the sum of the squares on the legs of a right triangle will be equal to the square on the hypotenuse.



a2 + b2 = c2

or

leg2 + leg2 = hypotenuse2

For the purposes of this course, a2 + b2 = c2 will be the main formula used for calculations. Sides a and b are interchangable. Side c is always the hypotenuse.

The Pythagorean Theorem only applies to right angle triangles. If a triangle does not contain a right angle, the Pythagorean Theorem cannot be used.


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