Question

in a triangle ABC if AB =BC and D, E, and F are the midpoint of the sides AB, BC and CA respectively then prove that DE =EF.

Answer 1

In triangle ABC, by Midpoint Theorem,
DE // AC and DE = 1/2 AC, (equation 1)
EF // AB and EF = 1/2 AB,(equation 2)
DF = BC and DF = 1/2 BC (equation 3)
Therefore AB = BC = CA
Then from equations 1 and 2 we have 1/2 AC = 1/2 AB
Therefore DE = EF

Answer 2

Answer:

Here we go with the answer: