1009.11 – Triangle Count

Count carefully; be systematic! The triangle $\triangle AEF$ has four more like it, $\triangle BAG,\triangle CBH, \triangle DCJ, \text{ and } \triangle EDK$, moving around the large figure clockwise. Similarly the seven additional triangles $\triangle AFB, \triangle AEB, \triangle ADH, \triangle AKC, \text{ and } \triangle ADC, \triangle AFG$ (all containing vertex $A$) each has four more around the large figure.

So the total number is 8 $\times$ 5 $=$ 40. (Have we counted anything twice? Have we missed any?)