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Question -

In a ABC, 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.



Answer -

  is given with E and F as the mid points of sides AB and AC.
 
Also,   intersecting EF at Q.
We need to prove that  
In  , E and F are the mid-points of AB and AC respectively.
Theorem states, the line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
Therefore, we get:  
Since, Q lies on EF.
Therefore,  
This means,
Q is the mid-point of AP.
Thus,   (Because, F is the mid point of AC and )
Hence proved.

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