Question

In a given quadrilateral, each side is parallel to its opposite side and the diagonals are not perpendicular. What could it be?

Answer 1

Rhombus

Explanation:

Assume a quadrilateral `ABCD`.
Given that `AB` `||` `CD` and `AD` `||` `BC`.
Also given that `AC_|_BD`.

If opposite sides of a quadrilateral are parallel, it's a parallelogram.

In a parallelogram diagonals intersect at their midpoints - let it be point `P`.

Consider now triangles `Delta ABP` and `Delta BCP`.
They are right triangles (since diagonals are perpendicular) and have two correspondingly congruent catheti: `AP = PC` and shared `BP`. Therefore, `AB=BC`.

Therefore, `ABCD` is parallelogram with all congruent sides, that is a rhombus.