Question

How many non-congruent triangles have vertices at three of the eight points in the array shown below?

$5$

$6$

$7$

$8$

$9$

By symmetry, it is enough to list one representative of each possible triangle shape.

One complete list of non-congruent possibilities is $AXY,$ $AXZ,$ $AXW,$ $AYZ,$ $AYW,$ $AZW,$ $BXZ,$ and $BXW$ .

Every other triangle formed from the eight points is congruent to one of these $8$ triangles.

Thus, D is the correct answer.