The Pythagoras Theorem

This applet demonstrates how to Pythagoras's Theorem (the Pythagorean Theorem) for right-angled triangles

UK Years 8-11, KS3, KS4, GCSE Mathematics, Grades C - A*, Shape Space and Measure
US Grade 9, Grade 10 - Geometry, Measure - Pre-Algebra

Instructions below    See also:   Simple Trigonometry

[Pythagoras Theorem (Pythagorean Theorem) for right-angled triangles]

On the screen you'll see a right-angled triangle. You can change this triangle by clicking and dragging the vertices (corner points) with the mouse, but it will always have a right-angle in it.
You can use this applet to investigate the Pythagoras Theorem (Rule), also called the Pythagorean Theorem, which applies only to right-angled triangles. If you know the lengths of two of the sides then you can use the rule to work out the length of the third side.
You can choose which of the three sides is "unknown" (ie the one you want to calculate) by checking one of the boxes at the bottom. The lengths of the other two sides are then shown.

If you have checked the "Show Working" box at the top of the screen you can then follow the working on the right to see the Pythagoras Theorem in action. Uncheck the box to hide the calculations if you want to.
Play around until you are sure that you understand how this very important theorem works. But remember, the theorem only works for right-angled triangles.