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3 years ago

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

Mathematics

1 answer:

Paha777 [63]3 years ago

4 0

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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