Question

BE IS PERPENDICULAR TO AC . AD IS ANY LINE FROM A TO BC INTERSECTING BE IN H .P,Q AND R ARE RESPECTIVELY THE MIDPOINTS OF AH,AB AND BC. PROVE THAT ANGLE PQR =90 DEGREE

Answer 1

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°


hopes this helps !!!!!!!!!

Answer 2

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