Converse of the Pythagorean Theorem

Students learn the Converse of the Pythagorean Theorem, which states that if the sum of the squares of the lengths of two sides of a triangle is equal to the sum of the square of the third side, then the triangle is a right triangle. Students also learn the following related theorems. If the sum of the squares of the lengths of two sides of a triangle is less than the sum of the square of the third side, then the triangle is obtuse. If the sum of the squares of the lengths of two sides of a triangle is greater than the sum of the square of the third side, then the triangle is acute. If the sum of the lengths of any two sides of a triangle is less than or equal to the length of the third side, then the triangle is not possible. Students are then given the lengths of the sides of a triangle, and are asked if the triangle is acute, right, obtuse, or not possible. A review of the Pythagorean Triples, such as 3-4-5 or 5-12-13, is also included in this lesson.