Example 3 As shown in Figure 3, in rectangle $A B C D$, it is known that the diagonal length is 2, and $\angle 1=\angle 2=\angle 3=\angle 4$. Then the perimeter of quadrilateral $E F G H$ is ().
(A) $2 \sqrt{2}$
(B) 4
(C) $4 \sqrt{2}$
(D) 6
(2010, Sichuan Province Junior High School Mathematics League (Grade 8))
As shown in Figure 3, according to the properties of axial symmetry, we know that the hypotenuse of $\triangle I J K$ is the perimeter of quadrilateral $E F G H$. The legs of the right triangle are twice the lengths of the sides of the rectangle. The diagonal of the rectangle and the two sides of the rectangle form a right triangle, so the perimeter of quadrilateral $E F G H$ is twice the length of the diagonal of the rectangle.