Step 1: Given $\triangle ABE \cong \triangle ACD$.
By CPCT (Corresponding Parts of Congruent Triangles) :
$$AB = AC \qquad \ldots (i)$$
$$AE = AD \qquad \ldots (ii)$$
Step 2: Divide $(ii)$ by $(i)$ :
$$\frac{AD}{AB} = \frac{AE}{AC}$$
Step 3: In $\triangle ADE$ and $\triangle ABC$ :
$$\frac{AD}{AB} = \frac{AE}{AC} \quad \text{(proved above)}$$
$$\angle DAE = \angle BAC \quad \text{(common angle } \angle A)$$
Step 4: By SAS similarity criterion,
$$\triangle ADE \sim \triangle ABC$$
Hence proved.