Polygon ABCD is a quadrilateral.

What would prove that ABCD is a parallelogram

Step-by-step explanation:

Parallelogram are square, rectangle, rhombus, and rhomboid and all with opposite lines that are parallel. Where each angle add up to 360. There are many quadrilaterals that are not parallelogram lesser known ones like convex quadrilaterals that are not parallelograms as they have no parallel lines and do not add up to 360. Polygons that intersect are not parallelograms. We can therefore show upon the parallelogram that there are 2 parallel lines within 4 lines of ABCD and if needed used in analogy with a 3 vertices triangle. Parallelogram like other quadrilaterals have 4 vertices but the angles of a parallelogram would alternate when drawn corner to corner. Diagonals must intersect at the opposite angle. We call them diagonals (not diagonal line) on a parallelogram, simply as where one crosses the other crosses and they become the plural.