Here's the solution to your geometry problem:
1. Prove that DE∣∣FC.
Step 1: Identify the relevant triangle and points.
Consider △AFC. Point D is on side AF, and point E is on side AC.
Step 2: Calculate the ratio DFAD.
We are given AFAD=53.
This means that AD is 3 parts and AF is 5 parts.
So, DF=AF−AD=5parts−3parts=2 parts.
Therefore, the ratio $\frac{AD}{DF} = \