Did you know that the right triangle is one of the most important geometric shapes and is foundational to the study of trigonometry?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
The ancient Greek mathematicians discovered that there were incredible relationships between the sides and angles of triangles, in particular, the right triangle.
One such discovery was the Pythagorean Theorem, named after the Greek mathematician Pythagoras.
The Pythagorean Theorem states that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
But in order to fully understand how to use the the theorem, we must first understand the terminology.
A right triangle is comprised of two legs and a hypotenuse, and the hypotenuse is the longest side and is always opposite the right angle. What this means, as Wikipedia accurately states, is that in any right triangle, the hypotenuse is greater than any one of the other sides but less than their sum.”
Formula for Using the Pythagorean Theorem
So when we solve right triangles for the missing side length, all we do is plug our given values into the Pythagorean theorem formula and solve the corresponding equation.
Simple!
But did you also know that the Pythagorean Theorem or the Pythagorean Equation as it is sometimes called is also used as a way to prove whether or not three numbers could represent the lengths of a right triangle?
By simply substituting the given values into the Pythagorean Theorem we can quickly verify whether the numbers represent a right triangle or an oblique triangle.
Together, we will learn how the this Theorem was created by looking at its proof, as well as learning how to use the formulas to solve missing side lengths of right triangles.
Pythagorean Theorem + Proof – Video
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