The Pythagorean Theorem states that for any right triangle with hypotenuse c and legs a and b:
a2 + b2 = c2
An example of a right triangle is shown below:
When using the Pythagorean formula, a2 + b2 = c2, a and b represent the legs, and c is always the hypotenuse.
We use the Pythagorean Theorem formula to find the length of a missing side of a right triangle. An example is shown below:
In this example, we know the lengths of the legs, which are 3 and 4. We do not know the length of the hypotenuse. We use the Pythagorean formula to substitute the values we do know to find the value we don't know:
Pythagorean Triples
Pythagorean triples are common integer lengths of sides we see in right triangles. The example above shows us the Pythagorean triple of (3, 4, 5). The biggest value is that of the length of the hypotenuse. If we remember some of the Pythagorean triples, it can make solving Pythagorean Theorem problems quicker and easier.
Other examples of Pythagorean triples include: (5, 12, 13), (7, 24, 25), and (8, 15, 17)
Note that multiples of Pythagorean triples are also Pythagorean triples. For example, since (3, 4, 5) is a Pythagorean triple, so is (6, 8, 10). In this example, we multiplied all side lengths by a factor of 2.
These class notes provide further explanation on the Pythagorean Theorem, as well as some general review of triangles.
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