The square of the hypotenuse of a right angled triangle is equal to the sum of the squares on the other two sides
If we let c be the length of the hypotenuse and a and b be the lengths of the other two sides, the theorem can be expressed as the equation:
or, solved for c:
If c is already given, and the length of one of the legs must be found, the following equations can be used (The following equations are simply the converse of the original equation):
This equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found.
The area of the two smaller squares added together equals the area of the large square.
Here is an animated proof of the Pythagorean Theorem. TRY IT IN THE CLASSROOM BY DRAWING A RIGHT ANGLED TRIANGLE AND CUTTING THREE SEPARATE SQUARES OF PAPER EQUAL TO THE THREE SIDES (AS IN THE PICTURE ABOVE). CUT THE MIDDLE SIZE SQUARE INTO FOUR, CUTTING THROUGH THE CENTRE AND PARALLEL TO THE BIGGEST SQUARE, AND FIT ALL PIECES ONTO THE BIGGEST SQUARE. THEN THE SMALL SQUARE SHOULD FIT INTO THE SPACE, PROVING PYTHAGORAS THEOREM!