What is the Converse of the Pythagorean Theorem?

What is the Converse of the Pythagorean Theorem?

Note:

The converse of the Pythagorean Theorem is like the the Pythagorean Theorem in reverse. You can use it both forward and backward! Not all theorems work this way, but the Pythagorean Theorem does! This tutorial will show you how to use both the Pythagorean Theorem and its converse.

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Background Tutorials

  • Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

      • What are Acute, Obtuse, and Right Triangles?What are Acute, Obtuse, and Right Triangles?

      What are Acute, Obtuse, and Right Triangles?

      Did you know that there are different kinds of triangles? Knowing how to identify these triangles is an important part of solving many problems involving these triangles. Check out this tutorial and learn about some of the different kinds of triangles!

  • Explain a proof of the Pythagorean Theorem and its converse.

      • What is the Pythagorean Theorem?What is the Pythagorean Theorem?

      What is the Pythagorean Theorem?

      The Pythagorean theorem is a very popular theorem that shows a special relationship between the sides of a right triangle. In this tutorial, you'll get introduced to the Pythagorean theorem and see how it's used to solve for a missing length on a right triangle!

  • Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Further Exploration

  • Explain a proof of the Pythagorean Theorem and its converse.

      • How Do You Determine if a Triangle Is a Right Triangle if You Know its Sides?How Do You Determine if a Triangle Is a Right Triangle if You Know its Sides?

      How Do You Determine if a Triangle Is a Right Triangle if You Know its Sides?

      Think your triangle is a right triangle? Want to be sure? If you have the length of each side, apply the Pythagorean theorem to the triangle. If you get a true statement when you simplify, then you do indeed have a right triangle! If you get a false statement, then you can be sure that your triangle is not a right triangle. Check out this tutorial and learn how use the Pythagorean theorem to see if a triangle is a right triangle!