Year+10+Pythagoras

This is about right-angled triangles and working with the lengths of their sides. It is not about the sizes of the other angles in the triangle. That is covered in Trigonometry.

This is a cute little proof to show how it works:


It's about the areas of the squares that could be drawn on the sides. The Pythagoreans did not realise that it would also work with other similar shapes eg equilateral triangles on each side or semi-circles on each side.

If you need to, then draw the square on each side. The areas of the squares are added if you are trying to work out the length of the lloooonnnggggeeessstt side (called the hypotenuse). The areas of the squares are subtracted if you are trying to work out the length of one of the shorter sides.

This is a demo to show that the areas on the squares on the smaller sides add up to the area of the big square on the hypotenuse. Use the mouse to move individual points and watch the areas - they still add up. media type="custom" key="27528810" Have a look at the problems on ... there are squares drawn for you in order to help your understanding. After a while you won't need to draw the squares at all.