(2) As shown in the figure: (BD or AC is diagonal, E and F are on AD and BC, and EF vertically divides BD or AC).
Solution: Let the length of line segment ED be x, as shown in the figure.
The quadrilateral BFDE is a diamond.
∴ ED=BE=x
And ∵ AB=3, AD=4 in the rectangular ABCD.
∴ AE=4-x
In Rt△ABE, AE 2 +AB 2 =BE 2.
∴
Solution: x=, ∴ ED=?
∴
(3) Solution: As shown in Figure ∵ Folding ∴DF=EF Let the length of the line segment DF be X, then EF = X.
? ∫ad = 3 ∴af=3-x
? Point E is the midpoint of AB, and AB=2.
? ∴
In Rt△AEF, there are
∴
Solution: x=, ∴AF=?
In rectangular ABCD, due to folding in half,
∴∠D=∠FEM=90 .?
∴∠ 1+∠2=90 。 ?
∠∠A =∠B = 90。
∴∠ 1+∠3=90 。 ?
∴∠2=∠3
∴ ∽ ,
∴
∴BM=
∴
?
?