Proving Congruence in Isosceles Triangle Extensions

Consider an isosceles triangle $ABC$ where $AB = AC$. Extend the base $AC$ beyond point $C$ to select an arbitrary point $D$. On the segment $BD$, identify points $K$ and $L$ such that $\angle BDA = \angle KCD = \angle LAD$. Prove that the triangles $BCK$ and $ABL$ are congruent.