jmc

We may assume that one of the triangles is attached to side $\overline{AB}$. The second triangle can be attached to $\overline{BC}$ or $\overline{CD}$ to obtain two non-congruent figures. If the second triangle is attached to $\overline{AE}$ or to $\overline{DE}$, the figure can be reflected about the vertical axis of symmetry of the pentagon to obtain one of the two already counted. Thus the total is $\boxed{2}$.