Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

How would you move the bands on the pegboard to alter these shapes?