How many triangles can you make on the 3 by 3 pegboard?

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

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Cutting it Out

So, I started with a $10$ by $10$ green square,

I marked the half-way point along the top edge,

I then drew a line from that point to a corner at the base.

Then I cut the corner piece out along that line and made a change of colour, so I ended up with these two shapes:

What can you say about these two shapes?

Can you say something about the relationship between them?

Do you have any other ideas about these two shapes?

What about starting with a rectangle like this ...

Then you could mark it at half-way or elsewhere ...

What can you say now?