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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In Fig. 3,<Mathematics - Board Papers

In an equilateralRD Sharma - Mathematics