In the given fig. if AD `bot`BC
Prove that `AB^(2) + CD^(2) = BD^(2) + AC^(2) ` .

In the given figure , BD bot AC .Prove that AB^2 +CD^2 = AD^2 +BC^2

ABCD is a rhombus. Prove that AC^(2) + BD^(2) = 4 AB^(2)

In an equilateral triangle ABC, AD _|_ BC . Prove that : AB^(2) + CD^(2) = 5/4 AC^(2)

In the figure, If AC=BD then prove that AB=CD.

In Delta ABC , AD bot BC and AD^(2)= BD xx CD . Prove that AB^(2) + AC^(2) = (BD + CD)^(2)

In Delta ABC , BD : CD = 3 : 1 and AD _|_ BC . Prove that 2(AB^(2) - AC^(2)) = BC^(2) .

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

In Fig . ABC is a triangle in which angleABClt90^(@)and AD botBC. Prove that AC^(2)=AB^(2)+BC^(2)-2BC.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

In Fig. D is point on hypotenuse AC of Delta ABC , BD bot AC DM bot BC and DN bot AB . Prove that : (i) DM^(2) = DN . MC , (ii) DN^(2) = DM . AN