Question

prove that madians of an equilateral triangle are equal​

Answer 1

Step-by-step explanation:

Given: ABC is an equilateral triangle whose medians are AD, BE and CF. To Prove: AD = BE = CF

Proof: In Triangle ADC and Triangle BEC,

AC = BC

Triangle ABC is equilateral .: AB = BC = CA

ACD = BCE

A ABC is equilateral .: ABC = BCA = CAB = 60°

DE = EC

AD is a median

DC = DB =BC

BE is a median

EA = EC =AC

AC = BC

DC = EC

Triangle ADC =Triangle BEC

SAS congruence rule

AD = BE............c.s.c.t.

Similarly, we can prove that

BE = CF ..(2) =

and CF = AD ..(3)

From (1), (2) and (3)

AD = BE = CF

hence proved.