Consider the theorem from geometry:
“The sum of the squares of the sides of any quadrilateral exceeds the sum of the squares of the diagonals by four times the square of the length of the line segment which connects the midpoints of the diagonals.”
Deduce a theorem about vectors 
in 
based on this geometric theorem and prove it.
Incomplete.
2+2
∣∣A∣∣²+∣∣B∣∣²+∣∣C-A∣∣²+∣∣C-B∣∣² = ∣∣C∣∣²+∣∣A-B∣∣²+4 ∣∣ ½C – (B+½(A-B)∣∣²
Which is the same as: ||A∣∣²+∣∣B∣∣²+∣∣C-A∣∣²+∣∣C-B∣∣² = ∣∣C∣∣²+∣∣B-A∣∣²+ ∣∣A+B-C∣∣²