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Median

In an equilat...

Question

In an equilateral ∆ABC, AD ⊥ BC prove that AD² = 3BD².

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Solution

We have to prove that .

In right angled, using Pythagoras theorem we get,

….....(1)

We know that in an equilateral triangle every altitude is also median.

Therefore, AD bisects BC.

Therefore, we have

Since is an equilateral triangle,

Therefore, we can write equation (1) as

…......(2)

But

Therefore, equation (2) becomes,

Simplifying the equation we get,

Therefore, .

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