Question

prove apollonious theorem

Answer 1

Let in a ΔABC, D is the midpoint of BC.Prove that:

AB2+AC2=2CD2+2AD2

Given that BD=DC and we construct E such that AE=EC⟹AC=EC2 and DE||AB⟹DE=AB2

For the ΔDEC we have DC2=DE2+EC2⟹4DC2=AC2+AB2

we have AB2+AC2=2CD2+2CD2(1)

In ΔADE we have, AD2=AE2+DE2⟹AE2+DC2−EC2⟹AD2=DC2

Hence 2CD2=2AD2

Thus, we have

AB2+AC2=2CD2+2AD2

Please mark it as the brainliest!!!!!!