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How many different non-congruent isosceles triangles can be formed by connecting three of the dots in a 4x4 square array of dots?



Two triangles are congruent if they have the same traced outline, possibly up to rotating and flipping. This is equivalent to having the same set of 3 side lengths.

 Dec 16, 2019
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There are two triangles with a base of sqrt(2), two triangles with a base of 2 sqrt(2), two triangles with a base of 3 sqrt(2), and three triangles with a base of 2, for a total of 2 + 2 + 2 + 3 = 9 triangles.
 

 Dec 16, 2019

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