Can someone check this for me? . (b) suppose it is also known that ad ≅ cd. which postulate or theorem can be used to prove that δabd ≅ δcbd? i'm guessing it's the sas congruence postulate but i'm not very good at this so i'm not sure.

Yes it's SAS
AD = CD (given)
BD = BD (common side )
but since it didn't say AC丄BD
it's no way to prove the angels r 90° :/

but as it already given AD= CD
so it's proven that it's an isosceles triangle
therefore
∠BAD = ∠BCD (base ∠s isos. ∆)

therefore it's SAS (side angel side)

Hope this ; )