In triangle ABC if AD is the
median, then show that
A B ² + AC² = 2(AD² + BD²)
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Hey mate
Given: AD is a median in ABC.
To prove: AB2 + AC2 = 2[AD2 + BD2]
Construction: Draw AE BC
Proof:
In right triangles AEB and AEC, using Pythagoras theorem
AB2 + AC2 = BE2 + AE2 + EC2 + AE2 = 2AE2 + (BD - ED)2 + (ED + DC)2
= 2AE2 + 2ED2 + BD2 + DC2
AB2 + AC2 = 2AE2 + 2ED2 + 2BD2 [since BD = DC]
= 2 (AE2 + ED2 + BD2)
= 2 (AD2 + BD2)
[Using Pythagoras theorem in AED]
Hope this was helpful for you...
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