In figure, AD is a median of a triangle ABC and `AM bot BC.` Prove that

`AB ^(2) = AD ^(2)- BC. DM + ((BC)/( 2 )) ^(2)`

In figure, AD is a median of a triangle ABC and AM bot BC. Prove that AC ^(2) = AD ^(2) + BC. DM + ((BC)/( 2)) ^(2)

In figure, AD is a median of a triangle ABC and AM bot BC. Prove that AC ^(2) + AB ^(2) = 2 AD ^(2) + (1)/(2) BC ^(2).

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AC^2+AB^2= 2AD^2+1/2BC^2 . .

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AB^2=AD^2-BC.DM+((BC)/2)^2 . .

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AC^2=AD^2+BC.DM+((BC)/2)^2 . .

In figure, ABC is a triangle in which angle ABC gt 90^(@) and AD bot CB produced. Prove that AC ^(2) = AB ^(2) + BC ^(2) + 2 BC BD.

BL and CM are medians of a triangle ABC right angled at A. Prove that 4 ( BL^2 + CM^2 ) = 5 BC^2 .

In fig., ABD is a triangle right angled at A and AC bot BD. Show that:- AB^2 =BC.BD .

In Fig., ABD is a triangle right angled at A and AC bot BD . Show that: (i) AB^(2) = BC.BD (ii) AC^(2) = BC.DC (iii) AD^(2) = BD.CD

If ABCD is a quad, in which AB || CD and AD = BC. Prove that /_A = /_B .