Question

prove that triangle obtained by joining the midpoints of the sides of an isosceles triangle is also isosceles

Answer 1

Let the isosceles triangle be named as ABC where AB=BC and let D , E and F be the midpoints of sides AB, BC and CA respectively.

 

Now, F and E are midpoints => FE || AB and FE= 1/2 of AB.

 

Similarly, D and F are midpoints => DF || BC and DF=1/2 of BC = 1/2 of AB {Since AB=BC}

 

Therefore, in triangle DEF - EF=DF=1/2 of AB

Therefore triangle DEF is also isosceles.

Please refer the attachment for further clarification.

Hope This Helps :)