Video Crash Courses
Want to watch animated videos and solve interactive exercises about checking whether a triangle is a right triangle or not?
Click here to try Video Crash Courses called “The Pythagorean Theorem”!
The legs and the hypotenuse in a right triangle are connected through the Pythagorean theorem.
Formula
Pythagorean Theorem
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs:
Rule
The Two Uses of the Pythagorean Theorem
The Pythagorean theorem is mainly used for two purposes:
- 1.
- When you have a right triangle, you are going to find the length of one of the sides of the triangle, and you know the lengths of the other two sides.
- 2.
- When you have an arbitrary triangle, and you want to determine whether it’s a right triangle by testing if is the same as .
So, the theorem is used to find the sides of a right triangle, and to check whether a given triangle is a right triangle.
Example 1
You have a right triangle where , and . What is the length of ?
The hypotenuse is always the side of a right triangle opposite to the right angle—which is . You know, therefore, that is a leg of the triangle. You put this into the formula and find that
The length of side is 4.
Example 2
You want figure out if a triangle with sides 5, 8 and 9 is a right triangle.
You know that the hypotenuse is the longest side of a right triangle, so you find the square of the longest side:
Then, you find the sum of the squares of the other sides of the triangle
Since , you know for sure that this isn’t a right triangle.
