Question

In a $\Delta ABC,E$ 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 1

In $\Delta ABC,$ $E$ and $F$ are midpoints of sides $AC$ and $AB$ respectively.

$\therefore EF\parallel BC$

$\Rightarrow FQ\parallel BP$

$\Rightarrow$ $Q$ is the mid-point of $AP$

$\Rightarrow AQ=QP$

[$\because F$ is the mid-point of AB and $FQ\parallel BP$ ]