Question

prove that the medians of an equilateral triangle are equal​

Answer 1

Answer:

this is your answer ....

Answer 2

$\Large\underline{\underline{\sf \orange{Given}:}}$

In equilateral traingle whose medians are AD , BF , and CE .

$\Large\underline{\underline{\sf \orange{To\:Prove}:}}$

Medians of an equilateral traingle are equal

⛬ AD = BF = CE

$\Large\underline{\underline{\sf \orange{Proof}:}}$

In ∆ADC & ∆BFC

∆ABC is equilateral traingle

⛬ AB = BC = CA

In ∆ACD & ∆BCF

∆ABC is equilateral traingle

⛬ ∠ABC = ∠BCA = ∠CAB = 60°

DF = FC

AD is a medium

⛬ DC = DB = $\sf{\dfrac{1}{2}BC}$

BF is a medium

⛬ FA = FC = $\sf{\dfrac{1}{2}AC}$

Since , AC = BC

⛬ DC = FC

⛬⠀⠀⠀⠀⠀⠀⠀⠀⠀∆ADC = ∆BFC (SAS)

⛬ AD = BF $\huge{→}$ (1) (CPCT)

Similarly ,

BF = CE $\huge{→}$(2)

CE = AD $\huge{→}$ (3)

From eq 1 , 2 , 3

AD = BF = CE

Hence Proved ,

Medians of an equilateral triangle are equal