I understood, that comes from Godofredo V of Anjou and change the name of Anjou Plantagenet, by their dress. and just the Plantagenet reign in 1485, ushering in the tudor house. how true is this ?.
I'm afraid your question is confusing.
You are asking, in the title, 'How did the Plantagenet family become so powerful?' This is fine as a question.
The next sentence does not make sense thus no one can answer your question: 'how true is this?'