Diversity of Triangles

Geometry Level 2

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.

8 7 9 5 6

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1 solution

Kamal Khan
Nov 17, 2015

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.

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