jmc

There are $6$ points in the figure, and $3$ of them are needed to form a triangle, so there are $\left(\genfrac{}{}{0ex}{}{6}{3}\right)=20$ possible triplets of the $6$ points. However, some of these created congruent triangles, and some don't even make triangles at all. Case 1: Triangles congruent to $△RST$ There is obviously only $1$ of these: $△RST$ itself. Case 2: Triangles congruent to $△SYZ$ There are $4$ of these: $△SYZ,△RXY,△TXZ,$ and $△XYZ$. Case 3: Triangles congruent to $△RSX$ There are $6$ of these: $△RSX,△TSX,△STY,△RTY,△RSZ,$ and $△RTZ$. Case 4: Triangles congruent to $△SYX$ There are again $6$ of these: $△SYX,△SZX,△TYZ,△TYX,△RXZ,$ and $△RYZ$. However, if we add these up, we accounted for only $1+4+6+6=17$ of the $20$ possible triplets. We see that the remaining triplets don't even form triangles; they are $SYR,RXT,$ and $TZS$. Adding these $3$ into the total yields for all of the possible triplets, so we see that there are only $4$ possible non-congruent, non-degenerate triangles, $\boxed{4}$