Properties of Parallelograms

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. That single definition is all you need — every other property below follows from it, with no measuring required.

In any parallelogram:

opposite sides are equal in length;
opposite angles are equal;
consecutive angles add to 180^\circ — each pair of sides is parallel, so two angles next to each other are exactly a co-interior pair;
the diagonals bisect each other — each diagonal cuts the other exactly in half.

Why the angles work

Nothing here needs measuring — it all comes straight from "both pairs of sides are parallel". Step through a parallelogram ABCD and watch the angle facts appear.

Because AD \parallel BC with AB crossing them, the two angles at A and B are co-interior, so they add to 180^\circ. Slide round the shape the same way and you find the opposite angles at A and C must be equal.