We have a triangle ΔABC, given that BD is both the altitude and median of triangle ΔABC. It means BD⊥AC and AD=DC.
Now we have two Right triangles ΔBDA and ΔBDC such that:-
1. BD = BD (reflexive property)
2. ∡BDA = ∡BDC = 90° (because BD⊥AC; BD is altitude)
3. DA = DC ( because median BD bisects AC into DA=DC)
4. ΔBDA ≡ ΔBDC (Side-Angle-Side congruency of triangles)
5. BA = BC (CPCTC: corresponding parts of congruent triangles are congruent)
In triangle ABC, if AB = BC then we can say that ΔABC is an isosceles triangle.
Hence, option D i.e. Isosceles triangle is the final answer.
