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in Quadrilaterals by (56.3k points)

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.

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In a ΔABC 

E and F are mid points of AC and AB (Given) 

EF ∥ FE ⇒ EF = BC/2 and 

[By mid-point theorem] 

In ΔABP 

F is the mid-point of AB, again by mid-point theorem 

FQ ∥ BP 

Q is the mid-point of AP 

AQ = QP 

Hence Proved.

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