From ∠ BAC = 90, AB=AC=BD, ∠ Abd = 30.
∠CAD=∠DBE= 15
BE=AD,BD=AC。
So △DBE is equal to△ △CAD.
So ∠ACD=∠BDE, DC=DE, that is ∠ DCE = ∠ DEC = ∠ DBE+∠ BDE =15+∠ ACD.
45 =∠ACB =∠DCE+∠ACD = 15+2∠ACD。
So ∠ ACD = 15 = ∠ DAC.
That is, AD=CD