In ` A B C` , `A D` is a median. Prove that `A B^2+A C^2=2\ A D^2+2\ D C^2` .

A B C D is a rhombus. Prove that A B^2+B C^2+C D^2+D A^2=A C^2+B D^2

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .

In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^2=A C^2+B D^2 (ii) A B^2-B D^2=A C^2-C D^2

If A D is the median of A B C , using vectors, prove that A B^2+A C^2=2(A D^2+C D^2)dot

The perpendicular A D on the base B C of a triangle A B C intersects B C at D so that D B=3C D . Prove that 2\ A B^2=2\ A C^2+B C^2 .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

In /_\ A B C , given that A B=A C and B D_|_A C . Prove that B C^2=2\ A C * C D