Proved as follows:

∫△APC and△△△ BPD are equilateral triangles,

∴AP=PC,PD=PB,∠APD=∠CPB=60 +∠CPD。

∴△APD≌△CPB.(SAS)

∴AD=BC.

(By using the properties of equilateral triangle, the related conditions of congruence judgment are obtained: AP=PC, PD=PB, ∠ APD = ∠ CPB = 60+∠ CPD, and it is proved that △ APD △ CPB, so AD = BC. )