Prove that the medians of an equilateral triangle are equal.

To do:

We have to prove that the medians of an equilateral triangle are equal.

Solution:

Let in a $\triangle ABC, AD, BE$ and $CF$ are the medians of triangle and $AB = BC = CA$

In $\triangle BCE$ and $\triangle BCF$,

$BC = BC$                 (Common side)

$CE = BF$

$\angle C = \angle B$                       (Angles opposite to equal sides are equal)

Therefore, by SAS axiom,

$\triangle BCE \cong \triangle BCF$

This implies,

$BE = CF$            (CPCT)....…(i)

Similarly,

$\triangle CAD \cong \triangle CAF$

This implies,

$AD = CF$......…(ii)

From (i) and (ii)

$AD = BE = CF$

Hence proved.

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Updated on: 10-Oct-2022

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