Question:
In figure, 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°
Solution:
Given,
BE ⊥ AC and P, Q and R are respectively mid-point of AH, AB and BC.
To prove: ∠PQR = 90°
Proof: In ΔABC, Q and R are mid-points of AB and BC respectively.
∴ QR ∥ AC ..... (i)
In ΔABH, Q and P are the mid-points of AB and AH respectively
∴ QP ∥ BH ..... (ii)
But, BE⊥AC
Therefore, from equation (i) and equation (ii) we have,
QP⊥QR
⟹ ∠PQR = 90°
Hence Proved.