Math, asked by percyjackson5426, 11 months ago

In triangle ABC, if AD is the median, then show that AB^2+AC^2=2 (AD^2+BD^2)​

Answers

Answered by rastogi9473871573
0

Step-by-step explanation:

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Answered

In ABC, if AD is the median, then show that AB2 + AC2 = 2[AD2 + BD2].

Asked by Topperlearning User | 5th Dec, 2013, 10:24: AM

Expert Answer:

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]

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