2003 AMC 12B Problem 10

Assume one triangle is attached to side $AB.$ The second triangle can be attached to a side that is one step away or two steps away from $AB.$ Attaching it to $BC$ or $CD$ gives two figures; attaching it to $AE$ or $DE$ gives figures that are mirror images of these across the pentagon’s axis of symmetry. So there are only $2$ non-congruent figures. Thus, the correct answer is B.