illustration of why SSA may not prove congruence

SSA cannot be used to prove that two triangles are congruent when the angles that are known to be congruent are acute. Below is an illustration of how this can happen.

In the picture below, $\mathrm{△}ABC$ and $\mathrm{△}ABD$ share the angle $\mathrm{\angle }A$ and the side $\overline{AB}$, and the line segments $\overline{BC}$ and $\overline{BD}$ are congruent; however, $\mathrm{△}ABC$ and $\mathrm{△}ABD$ are clearly not congruent.