BE is perpendicular to AC.AD is any line from A to BC intersecting BE in H,P,Q and R are mid points of AH,AB and BC.Prove that angle PQR=90.
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Let ABC be a triangle.
We have BE⊥AC and AD is any line from A intersecting AE 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°
Cheers!!!!!!
We have BE⊥AC and AD is any line from A intersecting AE 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°
Cheers!!!!!!
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