AD = CD，∠ADC=60，

△ ADC is a regular triangle.

∴DC=CA=AD.

Turn the position of △ DCB 60 to △ACE clockwise around point C to connect EB.

∴db=ae,cb=ce,∠bce=∠ace-∠acb=∠bcd-∠acb=∠acd=60，

∴△CBE is a regular triangle.

∴BE=BC,∠CBE=60。

∴∠ABE=∠ABC+∠CBE=90。

In Rt△ABE, AE2 = AB2+ comes from BE2 of Pythagorean theorem.

∴BD2=AB2+BC2.