In a ΔABC, E and F are the mid-points of AC and AB respectively.
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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