In this tip we will use a Java applet¹ for you to play and observe different sizes of right and non-right triangles. Start by clicking on the "?" on the applet to get the instructions on how to work with the applet.

The idea is to click on any vertex of the triangle to change its shape and size. The bars and numbers on the right panel give you the dimensions of each of the sides. Make right triangles and try to find triangles where all three sides are whole numbers. One example is a triangle with sides 3, 4, and 5. Look for more. There should be about 4 different combinations. To help you out here are a few examples where two sides are given and you can find out the third one:

If you click on the "Large sizes" icon, then the sizes of the sides' lengths increase and you will be able to find more combinations.

Write down all the combinations that you find. Make a table with the headings a, b, and c, where c is the hypotenuse. When finding the triples, can you tell which of the numbers is the hypotenuse? The sets of three positive integer numbers in the table are referred to as the Pythagorean Triples. We will talk about these triples in the problems page later on.

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

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Once you have enough numbers in the table, look at them, analyze them, see if you find any way to relate them. How can you combine them in an equation?

If you think that you found a relationship that works with all the Pythagorean Triples, go ahead and click on the following icon to check if you did or did not find the relationship for which we are looking:

Ready for the next tip? Go ahead...