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Question
In Fig. below, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are
respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°.
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Solution
Given
BE ⊥ AC and P, Q and R are respectively midpoint of AH , AB and BC
To prove:
`∠`PQRD = 90°
Proof: In ΔABC, Q and R are midpoints of AB and BC respectively
∴QR || AC ......(i )
In ΔABH , Q and P are the midpoints of AB and AH respectively
∴ QP || BH
⇒ QP || BE ......(ii )
But, AC ^ BE ∴ from equation (i) and equation (ii) we have
QP ⊥ QR
⇒ `∠`PQR = 90°, hence proved.
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