Angle FED and CEB are vertical angles and therefore congruent.
Angle EDF and ECB are both right angles and there congruent.
Using the AA Similiarity Postulate, we can say that triangles FED and BEC are similar.
Now, we can use the idea that corresponding sides of similar triangles are proportional to find DF.
First, we know that the sides of the square have lengths of 7 as DE = 2 and EC = 5, so DC = 7.
So, side BC = 7 as well.
Set up a proportion:
\(\frac{DE}{CE}=\frac{DF}{CB}\\ \frac{2}{5}=\frac{DF}{7}\\ \frac{14}{5}=DF\)
DF = 14/5 or 2.8
