# Interpret this geometrically, as a statement about parallelograms.

1. Oct 10, 2011

### Jamin2112

1. The problem statement, all variables and given/known data

Prove that

|x+y|2 + |x-y|2 = 2|x|2 + 2|y|2

if x and y are elements of ℝk

2. Relevant equations

Ordinary stuff

3. The attempt at a solution

Got the first part, but I don't understand the parallelogram thing yet. The little sketch I drew didn't help.

2. Oct 11, 2011

### vrmuth

In a parallelogram the sum of squares of sides equals the sum of squares of its diagonals

3. Oct 11, 2011

### vrmuth

since $\left|X+Y\right|$ and $\left|X-Y\right|$ are diagonals of the parallelogram with $\left|X\right|$and $\left|Y\right|$ as the sides , it states the property
"In a parallelogram The sum of squares of diagonals equals the sum of squares of the sides"

Last edited: Oct 12, 2011
4. Oct 12, 2011

### Jamin2112

Drew the picture again. Now I understand it. Indeed: On a parallelogram, the sum of squares of diagonals equals the sum of squares of the sides