Balance is not symmetry

When I told my art teacher that I didn't really like their SmartBoard, and told them that it threw their room off balance, they told me "I'm no fan of symmetry." Just a few minutes ago, during Thanksgiving dinner, I realized that symmetry and balance are not the same thing. Yes, something symmetrical is balanced, but you can also have something that's balanced that isn't symmetrical.
For example, let's use numbers and a scale. On one side you have a three, seven, and five. On the other side you have a ten, four, and a one. Both sides add up to be fifteen, so they are balanced, but their values couldn't be more different.

Now I'll just wait for the turkey to kick in...