Question

D, E and F are the midpoints of the sides AB , BC and CA of an isosceles ∆ABC in which AB = BC prove that ∆DEF is also isosceles

Answer 1

Step-by-step explanation:

Given: △ABC, AB=BC, D, E and F are mid points of AB, BC and CA respectively.

Since, D is mid point of AB and E is mid point of BC

By Mid point theorem, DF∥AC and DF=21AC...(1)

Since, E is mid point of BC and F is mid point of AC

By Mid point theorem, EF∥AB and EF=21AB ...(2)

Hence, By (1) and (2)

DE=EF

or △DEF is an isosceles triangle.

Hope it was helpful for you

Answer 2

Given :-

D, E and F are the midpoints of the sides AB , BC and CA respectively of an isosceles ∆ ABC in which AB = BC.

To prove :-

∆ DEF is an isoceles triangle.

Proof :-

DF || AC

∴ DF = 1/2 AC ....(mid-point theorem) ___(i)

EF || AB

∴ EF = 1/2 AB ....(mid-point theorem) ___(ii)

Now,

On combining eq.(i) and (ii),

we get,

DF = EF.

∴ ∆ DEF is an isosceles triangle. (two sides of a triangle are equal)

_______________________proved..

@Miss_Solitary ✌️