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Prove that the medians of an equilate...

Prove that the medians of an equilateral triangle are equal.

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GIVEN A `DeltaABC" in which "AB=BC=AC and AD, BE` and CF are its medians.
TO PROVEV `AD = BE=CF`.
PROOF In `DeltaADC and DeltaBEA,` we have
`AC=BA" (given),"`
`DC=EA" "[because BC=AC rArr (1)/(2)BC=(1)/(2)AC]`
and `angleACD=angleBAE" "["each equal to "60^(@)]`
`therefore" "DeltaADC~=DeltaBEA" (SAS-criteria)."`
`therefore" "AD=BE" (c.p.c.t.)."`
Similarly, BE = CF.
Hence, AD = BE = CF.
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