Proof:
Let's start of by solving for the length of AC, which is just the sum of lengths AB and BC, which is 10 + 3 = 13 units.
Because of our second given, AC ≅ EG, we know that EG is also 13 units in length. Also, from our first given, BC ≅ EF, we know that EF is 3 units.
We also know that the length of EG is the sum of lengths EF and FG so we can write the equation
EG = EF + FG
13 = 3 + FG
FG = 10 meaning FG is 10 units