Question

*Method Required*

Prove that the medians of an equilateral triangle are equal.

Answer as per class 9 , Ch- Triangles
well explained answers will be appreciated :)

Answer 1

Heya !!
Here's your answer.. ⬇⬇

▶ Given :- In equilatera ∆ABC, AD, BE, CF are medians.

▶ To Prove :- AD = BE = CF

▶ Proof :-
AD is a median,
BD = DC = 1/2 BC

BE is a median,
AE = EC = 1/2 AC

Given that AC = BC so,
BD = AE
DC = EC --- ( 1 )


In ∆BEC and ∆ADC,

BC = AC --- ( equilateral side of ∆ )

angle BCE = angle ACD --- ( angles of equilateral triangle are equal )

DC = EC ---- ( from eq.1 )

Hence, ∆BEC = ∆ADC ( by SAS theo. )

AD = BE --- ( by CPCT ) ( 2 )

Similarly we can prove,

CF = AD --- ( 3 )

BE = CF --- ( 4 )

From eq.( 2 ), ( 3 ), and ( 4 ) we get...,

AD = BE = CF ----- ( Proved )


HOPE IT HELPS...

THANKS ^-^