Question

in a triangle ABC,angle B=90 and M is the midpoint of BC.prove that AC^2=AM^2+3BM^2

Answer 1

IT WILL HELP YOU. THIS IS THE MOST SIMPLEST METHOD

Answer 2

Answer:

Step-by-step explanation:

given,

BM = MC  (AM is median)

To prove,

AC^2 = AM^2 + 3BM^2

      Proof,

AC^2 = AB^2 + BC^2

        = AB^2 + ( BM + MC )^2

        = (AM^2 - BM^2)  +  BM^2 + MC^2 + 2BM.MC           (expand)

        Conveting all MC into BM   (BM=MC) ,

         = AM^2 - BM^2 + BM^2 + BM^2 + 2BM^2

         = AM^2 - BM^2 + 4BM^2

         = AM^2 + 3BM^2

HENCE PROVED