Converse of the Pythagorean Theorem
Explained w/ 11 Examples!

In today’s geometry lesson, you’re going to learn how to use the converse of the Pythagorean theorem.

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

More specifically, you’re going to use it to classify triangles and determine missing side lengths.

Let’s jump in!

The Pythagorean theorem is one of the most famous equations, as it helps us to relate the angle and sides of a right triangle.

Right Triangle Diagram

So when we solve right triangles for the missing side length, all we do is plug our given values into the formula and solve the corresponding equation.

Formula for Using the Pythagorean Theorem

Pythagorean Theorem Example

But did you know that we can determine whether or not a triangle is a right triangle, acute triangle, or obtuse triangle?

It’s true!

Just by examining its side lengths and using the converse Pythagorean theorem!

The theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

And the corollary states, if a triangle with side lengths a, b, and c where c is the length of the longest side, we can determine if the triangle is acute or obtuse.

We do this by comparing the sum of the squares of the legs is less than or greater than the square of the largest side, as Varsity Tutors accurately states.

Converse of Pythagorean Theorem Formula

Determine if it’s Right, Acute, or Obtuse

In the video below, you are going to review the Pythagorean theorem and its properties, and then use the converse of the Pythagorean theorem to determine if a triangle is a right triangle, acute triangle, or obtuse triangle.

In addition, you’ll learn a very important rule for setting up the converse equations. (Hint: Order Matters)

Video – Lesson & Examples

28 min

• Review of the Pythagorean Theorem (Examples #1-2)
• 00:04:21 – Understanding the Converse Pythagorean Theorem
• Exclusive Content for Member’s Only

• 00:06:47 – Classify the triangle as Right, Acute, or Obtuse (Examples #3-7)
• 00:17:38 – Use the Pythagorean theorem to find the missing length of the polygon (Examples #8-11)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions