Question

In $\Delta ABC,AB=AC.D,E$ and $F$ are mid-points of the sides $BC,CA$ and $AB$ respectively. then, $:$ $AD$ and $FE$ bisect each other$.$
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

Given: D, E, F are mid points of BC, CA and AB respectively. AB = AC
Let the point where AD and FE meet be G
Since, D and E are mid points of BC and CA respectively thus,
By mid point theorem, $DE\parallel AB$ and $DE=\frac{1}{2}AB$
In $△AFG$ and $△DEG$,
$\angle AGF=\angle DGE$ (Vertically Opposite angles)
$\angle FAG=\angle GDE$ (Alternate angles for parallel lines DE and AB)
$DA=DE$ (D is mid point of AB)
Thus, $△AFG\cong △DEG$ (ASA rule)
Hence, $AG=DG$ (Corresponding sides)
$EG=FG$ (Corresponding sides)
Thus, AD bisects EF