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In the given figure, BE 1 AC. AD is any line from A toBC intersecting BE at H. P, Q and R are mid-points ofAH,AB and BC respectively, then prove that |
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Answer» Let ABC be a triangle.We have BE⊥AC and AD is any line from A intersecting BE at H.P, Q and R are the mid points of AH, AB and BC respectively. Given Q and R are the mid points of sides AB and BC of ∆ABC respectively∴ QR||AC [Mid-point theorem]Given BE⊥AC∴ BE⊥QR In ∆ABH and Q and P are the mid points of sides AB and AH respectively.∴ QP||BH [Mid-point theorem]∴QP||BE⇒QP⊥QR (BE⊥QR)⇒∠PQR = 90° |
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