The Converse of the Pythagorean Theorem:
If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.
Will the following side lengths yield right triangles?
~ 3, 4, 5.......................... Yes/No
~ 5, 10, 12....................... Yes/No
~ 9, 40, 41....................... Yes/No
~ 18, 34, 39...................... Yes/No
~ 0.27, 0.36, 0.45.............. Yes/No
Pythagorean
Inequalities are 
. In other words,
if the leg squared plus the other leg squared equals the hypotenuse
squared, the triangle is a right triangle. If the sum of
the legs squared is less than the longest side squared, the triangle
will be acute.If the sum is greater than the longest side squared,
it will be obtuse.
Click here for a GSP demonstration.