Question

If D, E, and F are mid points of the sides AB, BC, and CA respectively of an isosceles triangle ABC, prove that Δ DEF is also isosceles. ​

Answer 1

Step-by-step explanation:

Given: D,E,F are the mid points of

AB,BC,CA

To Prove: DE = EF

Proof: AB = AC (isosceles triangle) ZB = ZC (angle opp to equal sides)

1/2 AB = 1/2 AC so,DB = CF

In AADF and ACEF

DB = CF (proved above)

BE = CE (E is the mid point of BC)

ZB = LC (proved above) .. AADF = ACEF (SAS)

DE = FE (CPCT)

Hence, Proved