Question

Given: Line XB bisects angle ABC; Line BX is an altitude. Prove: Line BX is a median.

Answer 1

Answer:

Step by step proof is given below.

Step-by-step 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.