Two rectangular pieces of paper with equal width are stacked together to get the quadrilateral ABCD as shown in the figure. (1) prove that quadrilateral ABCD is diamond; (2) if two rectangular pieces of paper are 8 in length and 2 in width, does the perimeter of diamond ABCD have a maximum or minimum? If it does, ask for it; if it does not, give a brief reason

Two rectangular pieces of paper with equal width are stacked together to get the quadrilateral ABCD as shown in the figure. (1) prove that quadrilateral ABCD is diamond; (2) if two rectangular pieces of paper are 8 in length and 2 in width, does the perimeter of diamond ABCD have a maximum or minimum? If it does, ask for it; if it does not, give a brief reason

(1) It is proved that: as shown in the figure, ∵ ad ∥ BC, DC ∥ AB, ∥ quadrilateral ABCD is parallelogram. Passing through points a and D respectively, AE ⊥ BC is e, DF ⊥ AB is f. ∵ the width of two rectangular pieces of paper is equal, ∵ AE = DF, and ∵ AE · BC = DF · AB = s ▱ ABCD, ≁ BC = AB, ▱ ABCD is diamond; (2) there is a minimum value