In triangle ABC if AD is the median then show that AB2 + AC2 = 2(AD2 + BD2)

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in triangle ABC, AD is median 

then , BD = BC 

in triangles ABD and ADC

AB2 = AD2 + BD2 .........(1)

AC2 = AD2 + BC2 ............(2)

now add both the equations,

AB2 + AC2 = AD2 + AD2 + BD2+ BC2

AB2 + AC2 = 2AD2 + 2BD2  [ since BD = BC]

AB2 + AC2 = 2[AD2 + BD2]

hence proved...

HOPE THIS WOULD HELP YOU OUT

  • -109
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