An easier solution to Euclid's Book I, Proposition 5?

Question

Proposition 5

Does not Common Notion 3 (If equals are subtracted from equals the remainders are equal) solve Proposition 5 all on its own?

1. Lines AB and AC are equal.
2. The base angles ABC and ACB are equal.
3. Extending lines AB and AC, and plotting points F and G gives us equal lines AF and AG.

Does it not follow that angles FBC and GCB are the remainders and therefore equal?