explain in your own words the difference between how the Pythagorean Theorem is used and how the converse of the Pythagorean Theorem is used.

Answer 1

Now wait a minute, you are asked to put this in your own words, not my words.

The theorem is:
If it is a right triangle then the sum of the squares of the two legs is equal to the hypotenuse squared.
How do you use that fact? For example if it is a right triangle with legs of 3 and 4, what is the length of the hypotenuse?
Then the converse:
If the square of the longest side is equal to the sum of the squares of the other two sides, then the angle opposite the longest side is a right angle.
So if you have a triangle with sides of 3, 4, and 5, how big is the angle opposite the side of length 5? What is an altitude of the triangle and therefore what is its area?