Answer :

Given in equilateral triangle ABC, AD BC.



We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.


Now, in right triangle ADC,


AC2 = AD2 + DC2


BC2 = AD2 + DC2 [ AC = BC]


(2DC)2 = AD2 + DC2 [ BC = 2DC]


4DC2 = AD2 + DC2


3DC2 = AD2


3CD2 = AD2

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