The Pythagorean Theorem
The Pythagorean Theorem, a^{2} + b^{2} = c^{2}, is probably the most famous and wellknown formula in all of mathematics.
Pythagoras is credited with discovering the relationship between the sides of a right triangle, but the truth is highly debated. Regardless, the theorem is used frequently used, so it is very important that you know it!
Pythagoras 


Right Triangles: The Legs and the Hypotenuse 
First of all, the pythagorean theorem can only be used in right triangles. In all triangles there are three sides; in a right triangle, two of those sides are known as the legs and the other side is known as the hypotenuse.
The hypotenuse is the largest side of the triangle, which is always across from the right angle. The other two sides are the legs and it doesn't matter which one is which. Take a look at the examples below...
Notice the arrows above pointing across from the right angle to the hyptoenuse. The hypotenuse is important because it is the c value.
The legs represent the a and the b values: again, it doesn't matter which one is which. In a sense, the theorem is really...
leg^{2} + leg^{2} = hypotenuse^{2} 


To use this theorem, subsitute the two values that you know, and solve for the missing one. Make sure you place the hypotenuse in the right location! 

Take a look at the examples below. Again, notice how the hypotenuse is always substituted in for c (the right side of the equation).
It's as easy as that! Congratulations, you now know how to use the pythagorean theorem. Return to more free geometry help o r visit the GradeA homepage for other free math help resources.
