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Question
In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.
Solution
In ΔBXD and ΔCYD
∠BXD = ∠CYD ...(90)
∠XDB = ∠YDC ...(vertically opposite angles)
BD = DC ...(AD is median on BC)
Therefore, ΔBXD ≅ ΔCYD ...(AAS criteria)
Hence, BX = CY.
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