How To Verify A Triangle Is A Right Triangle Using The Pythagorean Theorem Explained

Описание: In this video we discuss how to use the Pythagorean theorem to verify a triangle is a right triangle. We go through a few examples showing the process.

Transcript/notes
When we are given the lengths of the 3 sides of a triangle and we want to verify the triangle is a right triangle, where one of the angles is equal to 90 degrees, we use the Pythagorean theorem.

The formula for the Pythagorean theorem is c squared equals a squared plus b squared. In this formula, c is the length of the hypotenuse, or the side opposite the 90 degree angle in a triangle. And a and b would be the length of the sides that connect to form the 90 degree angle in a triangle, which are often referred to as legs.

As an example, let’s say that we are given a right triangle with sides of lengths 5.25, 7 and 8.75, and we need to verify that this is a right triangle. To do this, we use the variables from the Pythagorean theorem of c squared equals a squared plus b squared.

We first square all of the lengths of the sides. So, we have 5.25 squared, which equals 27.5625, next is 7 squared, which equals 49, and then 8.75 squared, which equals 76.5625.

So, we next ask ourselves, do adding the 2 smaller numbers together, equal the larger number?

do adding together any of these 2 numbers equal the other number? By inspection, we can see that if we add together 27.5626 and 49, we get 76.5625. And we can assign a to be 7, b to be 5.25 and c, the hypotenuse, to be 8.75 squared. And indeed, we can verify that this triangle is a right triangle.

The key to verifying a right triangle is to square all of the lengths of the sides and check if adding together any of the 2 numbers equal the other number.
Here are a couple more examples of verifying a right triangle.

Timestamps
0:00 Intro
0:10 Formula for Pythagorean theorem
0:30 Example of verifying a right triangle
1:32 Keys to verifying a right triangle
1:42 More examples of verifying a right triangle