March 10: Converse of Pythagorean Theorem

Today we looked at the Converse of the Pythagorean Theorem.

Before we do that, let's consider what the Pythagorean Theorem is, because it's not JUST a² + b² = c²

The Pythagorean Theorem can be written as follows:

If a triangle IS a right triangle, then a² + b² = c².

The Converse states:

If a² +b² = c², then the triangle IS a right triangle.

Wait... isn't that the same thing?

Nope!  Think about it this way:

If it's the weekend, then we don't have school.  

What is the converse of that statement?

If we don't have school, then it's the weekend.

Is that true?  Not necessarily!  So the converse of the Pythagorean Theorem may at first seem like the exact same thing, but it really isn't!

We can use the converse to determine if a triangle is a right triangle.  If we know the side lengths, we put them into the formula and determine if the sides do in fact create a right triangle!

Click here for tonight's homework.