I see that you have uploaded a mathematical problem. Let me analyze the image and assist you with the solution.

The problem involves triangle $ABC$, where $A$ is the vertex of the triangle, and points $D$ and $E$ lie on sides $AC$ and $AB$ respectively, such that $AD = AF$. The questions involve proving the following:

a) Proving $\triangle ADB = \triangle AEC$. b) Let $I$ be the intersection of lines $BD$ and $CF$. What type of triangle is $IBC$? Justify your answer. c) Prove that $ED \parallel BC$.

I will go through each of these in detail. Do you want me to start solving them one by one or would you like a broader explanation of the overall approach first?