Pythagorean Theorem:
According to Pythagorean's Theorem: in a right triangle, the sum of the squares of the length of each leg is equal to the square of the hypotenuse, or:
where a and b are legs and cis the hypotenuse.
How Can We Use the Pythagorean Theorem:
The Pythagorean Theorem only applies to right triangles. This means that we can use the theorem to determine if a triangle is a right triangle if given its sides.
Additionally, if given a right triangle, and any two sides, we can find the length of the third. This is often used to find distances and heights using known quantities.
If we have the lengths of both legs, we can find the sum of the squares to get the square of the hypotenuse. If we have the hypotenuse and one leg, we can subtract the squares to get the square of the missing leg.
Pythagorean Triples
Pythagorean Triples are groups of three whole numbers that satisfy the Pythagorean Theorem. There are an infinite number of these. Multiples of Pythagorean Triples are also Pythagorean Triples. (3, 4, 5) is a Pythagorean Triple, this means that (6, 8, 10) is also a Pythagorean triple, since all three sides are multiplied by 2.
Sample Math Problems
Example 1:
Example 1: Use the Pythagorean Theorem to determine if the triangle with side lengths 9 cm, 12 cm, and 15 cm is a right triangle.
Solution:
Looking at the numbers, 15 cm is the largest side length, so c=15 cm. Since Addition is commutative, then 9 cm and 12 cm can be either a or b. In this case, let a=9 cm and b=12 cm. Now we can apply the Pythagorean Theorem:
