Add △ABC to the square to connect DE, and it is easy to prove that △BDE is an equilateral triangle, ∠ Bader = ∠ BDA = ∠ EDC = ∠ ECD = 75.

∠DAC=∠DCA= 15 ,∴AD=CD

PS: This is actually the first question in the final of the 20 10 Beijing senior high school entrance examination.