Question

In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.

Answer 1

In ΔBNC and ΔCMB
∠BNC = ∠CMB = 90°
∠NBC = ∠MCB  ...(AB = AC)
BC = BC
Therefore, ΔBNC ≅ ΔCMB  ...(AAS criteria)
Hence, BM = CN.