Pythagorean Inequalities Theorem
Definition: Suppose that there is a Triangle ABC in which Sides A & B are the legs, and Side C is the longest side. If C^2>A^2+B^2, then the triangle is an obtuse triangle, and if C^2<A^2+B^2 then the triangle is an acute triangle.
Symbol/Notation: none
Statement: Although the angles of the triangle shown above are not given, we can still determine whether the triangle is an acute, obtuse, or right triangle. 7^2=49, 12^2=144, =144+49=193, 14^2=196, and 196>193. With our calculations, and by using the Pythagorean Inequalities Theorem, we can conclude that this triangle is an obtuse triangle.