The Pythagorean Theorem Converse & Triangle Inequality Theorem  Pythagoras, circa 570 BC.

Pythagorean Theorem Review  In a right triangle, the sum of the squares of each leg equals the square of the hypotenuse.

Pythagorean Theorem Review  Therefore, in this triangle, the legs are a and b. The hypotenuse is c. So, the pythagorean theorem states: a 2 + b 2 =c 2

Pythagorean Theorem CONVERSE  The Pythagorean Theorem ONLY works for right triangles. Therefore, the converse of the Pythagorean Theorem is true. The converse reads…if a 2 + b 2 =c 2, where c is the longest side of a triangle, then the triangle is a right triangle.

Pythagorean Theorem CONVERSE  So, if you don’t know if the triangle is a right triangle, but the Pythagorean Theorem “works”, then it IS a right triangle.  Example: If a = 3, b = 4, and c = 5, is the triangle a right triangle? Work out the Pythagorean theorem on your paper.

Pythagorean Theorem CONVERSE  a 2 + b 2 ? C 2  ? 5 2  ? 25  25 = 25 …..So, the triangle IS a right triangle!

Pythagorean Theorem CONVERSE  A triangle has side lengths of 6, 7, and 10. Is the triangle a right triangle?

REMEMBER! The Pythagorean Theorem ONLY works for RIGHT triangles!

The Triangle Inequality Theorem  IN ANY triangle, the sum of any 2 sides MUST be larger than the third side!  If this doesn’t occur, you will not be able to create ANY kind of triangle.  Example: You have wood that is 3cm, 5cm, and 9 cm long. Can you create a triangle with these 3 pieces of wood?

The Triangle Inequality Theorem  NO. You could NOT create a triangle.  = 8. 8 is not bigger than 9, so you would have 2 pieces that would not connect!

REVIEW REVIEW  The PYTHAGOREAN THEOREM ONLY WORKS FOR RIGHT TRIANGLES.  THE SUM OF ANY 2 SIDES OF A TRIANGLE MUST BE LARGER THAN THE THIRD SIDE.