Let `A B C` be an isosceles triangle with `A B=A C` and let `D , E ,F` be the mid-points of `B C ,C A` and `A B` respectively. Show that `A D_|_F E` and `A D` is bisected by `F Edot` `"

Explanation

`"Join the points DE, EF, FD & AD"`

`therefore DE "//" AB
, DE=1/2AB("By Midpoint theorem")`

`DF "//" AC , DF=1/2AC("By Midpoint theorem")`

`Given: AB = AC, therefore 1/2AB = 1/2 AC => DE=DF`

`DE=1/2AB=DE=AF`

`DF=1/2AC=DF=AE`

`therefore DE=AF=DF=AE`

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