Pythagorean Theorem
Pythagorean Theorem is quite important in math. The formula -- a²+b²=c² -- will determine whether a triangle is a right triangle, determine the side of a right triangle, and much more than you can imagine. But explaining all of those things would take forever, so we're only going to be learning about the first two functions listed.
In the formula of the Pythagorean Theorem, a and b represent the legs of the right triangle. That is the two shortest sides of the triangle, which would be coming out from the right angle if the triangle were to be a right triangle. Equally important, there is c, which is called the hypotenuse of the triangle. This would be the longest side of the right triangle, always opposite of the right angle. If the sum of a² and b² is c², the triangle is a right triangle.
In the formula of the Pythagorean Theorem, a and b represent the legs of the right triangle. That is the two shortest sides of the triangle, which would be coming out from the right angle if the triangle were to be a right triangle. Equally important, there is c, which is called the hypotenuse of the triangle. This would be the longest side of the right triangle, always opposite of the right angle. If the sum of a² and b² is c², the triangle is a right triangle.
A Brief History of the Pythagorean Theorem
Pythagoras lived in ancient Greece and formed a group called the Brotherhood of Pythagoreans, devoted to mathematical studies. He believed that numbers ruled the world. Legend says that he was credited with the discovery of the Pythagorean Theorem, though we can't tell if he's is the actual author of the theorem.
Pythagorean Theorem Example
If a=3, and b=4, what is c?
a²+b²=c² → write out the formula
3²+4²=c² → fill in with given numbers
9+16=c² → simplify the exponents
25=c² → add the numbers
√25=c → find the square root of each side, to take away the exponent on the right
c=5 → simplify
a²+b²=c² → write out the formula
3²+4²=c² → fill in with given numbers
9+16=c² → simplify the exponents
25=c² → add the numbers
√25=c → find the square root of each side, to take away the exponent on the right
c=5 → simplify
Pythagorean Theorem Practice Problem
If a triangle has a side length, a, of 5 inches, another side length, b, of 12 inches, and another side, c, which is 14 inches long, is the triangle a right triangle?
Answer Key
Answer Key
