Let $ABCD$ be a unit square. Four points E,F,G, and H are chosen on the sides $AB,BC,CD,$ and $DA$ respectively. Let the length of the quadrilateral be $a,b,c,d$. Then which of these is always true?
1) $1\leq a^2+b^2+c^2+d^2 \leq 2\sqrt{2}$
2) $2\sqrt{2} \leq a^2+b^2+c^2+d^2\leq 4\sqrt{2}$
3) $2\leq a^2+b^2+c^2+d^2 \leq 4$
4) $\sqrt{2} \leq a^2+b^2+c^2+d^2 \leq 2+\sqrt{2}$
Hints should suffice to get me started. Thanks.