If we think about a right triangle we know of course that one of the angles is a right angle. We also know that the other two angles are acute angles (why?). In fact we know that the other two angles are complementary angles. Therefore there is a relationship between the sizes of the angles that the two acute angles have measures that add up to ninety degrees.

What about sides? Is there a relationship between the sides of a right triangle? We know from previous lessons that if we have the lengths of just two of the sides we can construct the triangle so it is enough to know the lengths of two sides to determine the length of the third side. We shall now try to figure out the relationship. We shall, to make it easy to communicate assume that the length of the hypotenuse is c units and that the two legs are of length a and b units.
In the applet below we have a right triangle and we can change the lengths of the sides by dragging the red vertices with the mouse. change the lengths of the sides of the right triangle. 

• Draw a graph of a versus b. What does the graph seem to be?
• Draw a graph of a² versus b² . This time the points would suggest a line. What is the slope of this line? Try to guess what the relationship between a², b², and c² is.