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The Mid-Point Theorem

In Δ ABC , AD...

Question

In ∆ABC, AD is a median. Prove that AB² + AC² = 2AD² + 2DC².

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Solution

We have the following figure.

Since triangle ABM and ACM are right triangles right angled at M

…… (i)

…… (ii)

Adding (i) and (ii), we get

Since in triangle ADM we have

So,

BM + CM = BC

So,

Now we have

So,

Hence proved

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A B^{2} + A C^{2} = 2 A D^{2} + 2 B D^{2} ?

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ABC, AD is a median. Prove that

{A B}^{2} + {A C}^{2} = 2 ({A D}^{2} + {D C}^{2}) .

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