Question

How did the prince know that the girl he was trying to find was Cinderella

Answer 1

In the usual versions of the tale (Perrault/Disney), Cinderella leaves behind one of her shoes at the ball — famously a glass slipper. The prince keeps that shoe and has every eligible young woman try it on; it fits only Cinderella, proving she is the mysterious dancer he’s been searching for.

(Variants: in some older or Grimm versions the shoe is made of gold or leather rather than glass, and the stepsisters try to force or trick the fit; in the Grimm tale birds ultimately expose the deception. But the core identification device across versions is the shoe fitting her foot.)