Prove that triangle ADE is similar to triangle ABC.

Here's how to solve the problem:

Step 1: Identify the similar triangles.
The diagram shows a smaller triangle at the top and a larger triangle encompassing it. Since the line segment forming the base of the smaller triangle is parallel to the base of the larger triangle (implied by the common angle at the top vertex and the geometry), the two triangles are similar by the Angle-Angle (AA) similarity criterion.
Let the top vertex be $A$. Let the vertices of the smaller triangle be $A$, $D$ (on the left side), and $E$ (on the right side). Let the vertices of the larger triangle be $A$, $B$ (on the left side), and $C$ (on