Millennium Park has an outdoor concert theater. Before a concert, the area reserved for special seating is roped off in the shape of a triangle as shown below. How can the converse of the Pythagorean theorem help you determine whether the roped off area is in the shape of a right triangle?
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Home » Triangle Trig » Converse Pythagorean Theorem
Converse of the Pythagorean Theorem
Explained w/ 11 Examples!
// Last Updated: January 21, 2020 - Watch Video //
In today’s geometry lesson, you’re going to learn how to use the converse of the Pythagorean theorem.
Jenn (B.S., M.Ed.) of Calcworkshop® teaching converse 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.
And as we know, a right triangle is comprised of two legs and a hypotenuse.
The hypotenuse is the longest side and is always opposite to the right angle.
right triangle diagram
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.
Understanding how to use the pythagorean theorem to find missing side lengths of a right triangle
Formula for Using the Pythagorean Theorem
pythagorean theorem example
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!
What is the Converse of the 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
Converse of Pythagorean Theorem Formula
how to determine if a triangle is right acute or obtuse based on side lengths
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