Diversity of Triangles
How many
non-congruent triangles
have vertices at three of the eight points in the figure above?
Details and Assumptions: Two triangle are congruent if one can be transformed into the other via an isometry: rotation, reflection, and translation are all isometries.
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1 solution
A* B* C* D*
E* F* G* H*
1) Right angled triangles -> ABE, ACE,ADE
2) Other Triangles -> EBG,EBH,AFG,AGH,AFH
All other triangles except these 8 can be transformed into one of the triangles in the solution set.