Question

Can someone check this for me? Thanks.

(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.

Answer 1

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)