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 △ BDA and △ 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 △ BDA and △ 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.
