Let `A B C` be an isosceles triangle in which `AB=AC` If `D , E , F` be the mid-points of the sides `B C ,\ C A\ a n d\ A B` respectively, show that the segment `A D\ a n d\ E F` bisect each other at right angles.

Explanation

in `/_\ABC` ,E , F and D
are the mid-points of `A C, A B, BC` respectively.

A D intersects B C


join D to E

now in AFDE, `DE||AF`

and both are equal so but
here `AF=DE`and `AF=AE`

so all sides of AFDE are equal to each other so it is a rhombus and diagonal of a
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