CBSE Class 9 Answered

Dear Student

Say A=2θ and AC=AB=2x  ==>  EAG= θ ,  AE=x.

Since ABC in Isosceles = B=C= (180-A)/2 = (180-2θ)/2=90-θ

In any riangle a segment joining mid points of two sides is parellel to the third side

==> EF//BC  ==> AEF =C = 90-θ 

In an isosceles triangle angle between equal sideas is bisecteb by line joining to the opposite side 

==>  GAF=θ 

In the triangle AGE

   A +G+E =180  ==>θ +G+90-θ   

==>

G= 90

So,the segment AD&EF bisect each other at right angles

Regards

Topperlearning