In an equilateral triangle ABC if , then
Given in equilateral triangle ABC if 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 ABD,
⇒ AB2 = AD2 + BD2
⇒ AB2 = AD2 + ( � BC)2 [∵ BD = �BC]
⇒ AB2 = AD2 + ( � AB)2 [∵ AB = BC]
⇒ AB2 = AD2 + ( �AB)2
∴ 3AB2 = 4AD2