Example 7 As shown in Figure 6, in rectangle $ABCD$, it is known that the diagonal length is 2, and
$$
\begin{array}{l}
\angle 1=\angle 2= \\
\angle 3=\angle 4 .
\end{array}
$$

Then the perimeter of quadrilateral
$\mathrm{EFGH}$
is ( ).
(A) $2 \sqrt{2}$
(B) 4
(C) $4 \sqrt{2}$
(D) 6
(2010, Sichuan Province Junior High School Mathematics Competition)
Solution 1 According to the reflection relationship, as shown in Figure $6, \mathrm{Rt} \triangle I J K$'s hypotenuse is the perimeter of quadrilateral $E F G H$, and the right-angle sides are twice the length of the rectangle's sides, therefore, the perimeter of quadrilateral $E F G H$ is twice the length of the rectangle's diagonal.
Enemy choice B.
Solution 2 Take $E, F, G, H$ as the midpoints of each side, at this time, quadrilateral $E F G H$ satisfies $\angle 1=\angle 2=\angle 3=$ $\angle 4, \mathrm{H} H E=E F=F G=G H=1$.
Therefore, the perimeter is 4.