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.  

March 5: Pythagorean Theorem

Today was the first day of Pythagorean Theorem.  We learned that the sum of the squares of the legs is equal to the square of the hypotenuse.  What?  Here's a better explanation with an example:

We saw a video proof of Pythagorean's Theorem as well.  When squares are created using the sides of a right triangle, we saw that when the wheel was turned over, the water in the two squares along the legs fill the square along the hypotenuse perfectly.

The equation for solving right triangles is 

a² + b² = c²

^{Click here for today's homework}