The diagram shows an isosceles triangle.
Let's modify it a bit to highlight that AB< BC.
Now we should summarize what we know about triangles â–³ BDA and â–³ BDC.
Claim
Justification
AB< BC
Given in the question.
AD≅CD
BD is a median, so D is a midpoint of AC.
Since BD is a common side of triangles â–³ BDA and â–³ BDC, these triangles have two pairs of congruent sides.
This means that we can use the Converse of the Hinge Theorem.
AB< BC
⇓
m∠BDA< m∠BDC
Since ∠BDA and ∠BDC form a linear pair, their measures add to 180.
If m∠BDA< m∠BDC, this can only happen if m∠BDA<90 and m∠BDC>90.
The consequence of this is that angle ∠BDC is obtuse, and it is neveracute.
