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Triangular Tantaliser

Age 11 to 14
Challenge Level

Here is a 4 by 4 dotty grid:
Picture of a Geoboard with four rows of four pegs

How many different triangles can you draw by joining dots on the grid?
We count two triangles as the same if you can cut one out and fit it exactly on top of the other.

Can you come up with a convincing argument that you have found all the possible triangles?