You might find it useful to use one or more of the following:
- Spotted paper in squares 
- Nail boards with elastic bands
- The on-screen interactive board
- Squared paper.

You could try finding all the different right-angled triangles by moving one point first, then moving a second point, then the third.
Why not try with the top left corner to start with? Where could this point move to?
How will you kow that you have them all?
Have you decided how to record your work?