In this last tip we again use a Java applet. If you look at it, it is essentially the same that we used before except for one important difference. On the right panel, instead of displaying the lengths of each of the sides of the triangle it displays the squares of the lengths.  So for example, whereas the previous applet showed you the combination (or Pythagorean triple, right?) of 3, 4, and 5, this one will display 9, 16, and 25.

Not only does this version show you the squares of the lengths, but it shows the longest side by itself, which in most cases is the hypotenuse (or the c side). It also combines the other two in a single column. You could say that it adds them together. Interesting, right?

You should have read the instructions for the applet already, so you can go ahead and use it.

---

If your browser recognized the applet tag, you would see an applet here.

---

You probably already figured out the famous theorem. If you haven't, I suggest that you make any right triangle and observe the right panel. Then move the top vertex to the right and to the left and see what happens. Go back to the right triangle and check the right panel again. Did you get it?

The most interesting thing is that:

The theorem holds true for any right triangle!

Go ahead and try as many as you want. Change the scale and try some more. It always holds true! Now, in case you haven't tried the little test, here is you last opportunity:

You can now go back through all the five tips, especially the ones where you hadn't figured it out, and re-check them. They should make sense now.

Once you have finished you can go ahead to the next page and record how you did. Compare your results with those of all the previous students.