In an equilateral ` A B C` , `A D_|_B C` , prove that `A D^2=3\ B D^2`

In an equilateral triangle A B C if A D_|_B C , then

In an equilateral triangle A B C , if A D_|_B C , then (a) 2\ A B^2=3\ A D^2 (b) 4\ A B^2=3\ A D^2 (c) 3\ A B^2=4\ A D^2 (d) 3\ A B^2=2\ A D^2

In an equilateral triangle A B C if A D_|_B C , then A D^2 = (a) C D^2 (b) 2C D^2 (c) 3C D^2 (d) 4C D^2

In an equilateral triangle A B C if A D_|_B C , then A D^2 = (a)C D^2 (b) 2C D^2 (c) 3C D^2 (d) 4C D^2

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

If A B C D is a quadrilateral in which A B C D and A D=B C , prove that /_A = /_B .

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 .

A point D is on the side B C of an equilateral triangle A B C such that D C=1/4\ B C . Prove that A D^2=13\ C D^2 .

If A B C is an equilateral triangle such that A D_|_B C , then A D^2= (a) 3/2D C^2 (b) 2\ D C^2 (c) 3\ C D^2 (d) 4\ D C^2