Question:
In a ΔABC, E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects FE at Q. Prove that AQ = QP.
Solution:
In a ΔABC
E and F are mid points of AB and AC
∴ EF ∥ FE, (1/2) BC = FE [By midpoint theorem]
In ΔABP
F is the mid-point of AB and ∴ FQ ∥ BP [∴ EF ∥ BP]
Therefore, Q is the mid-point of AP [By mid-point theorem]
Hence, AQ = QP.
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