Can you make 10 triangles with just 10 sticks?
The sticks don't have to have the same length.
Try making 4 triangles with 6 sticks of equal length. Now put more shorter sticks inside this shape.
If the world would have four or more dimensions, you could have made the shape with sticks that have exactly the same length.
There are several other possibilities than the one I gave hints for.
I recently found one with at least 40 triangles. However, for that, overlapping sticks are needed. Why not try searching for the greatest amount of triangles?
If you disallow overlapping sticks, 13 triangles is possible.