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