Answer:
Step by step proof is given below.
Explanation:
∠ABX = ∠XBC (given that XB bisects ∠ABC)
∠AXB = ∠CXB = 90° (given that BX is an altitude)
BX = BX (common)
Therefore,
ΔABX ≅ ΔCBX (ASA congruence theorem)
AX = CX (Corresponding parts of congruence triangles are congruent)
So, X is the midpoint of AC and hence BX is a median.