In quadrilateral ABCD, is AC longer than BD?

If A, B, C and D form a quadrilateral. Is AC > BD ?

(1) Angle ABC < Angle BCD

This tells us that ABCD is not a square or a rectangle because naturally, both have four angles each equaling 90 degrees. With a triangle, the leg across from the largest angle is the longest but does it work like that with a four sided figure? Apparently not because 1 is not sufficient.

(2) AB = BC= CD = DA

This tells us that ABCD is either a square or a rhombus. If the figure is a square, then both diagonals AC = BD. If the figure is a rhombus, then one diagonal will be longer than the other. Insufficient.

1+2) This tells us that all four sides are equal and that one angle (or in this case, pairs of angles) is greater than another. The only possible shape that has four equal sides and different interior angles is a Rhombus. AC > BD. Sufficient.