The properties of the parallelogram are simply those things that are true about it. These properties concern its sides, angles, and diagonals.

The parallelogram has the following properties:

- Opposite sides are parallel by definition.
- Opposite sides are congruent.
- Opposite angles are congruent.
- Consecutive angles are supplementary.
- The diagonals bisect each other.

If you just look at a parallelogram, the things that look true (namely, the things on this list) are true and are thus properties, and the things that don’t look like they’re true aren’t properties.

**If you draw a picture to help you figure out a quadrilateral’s properties, make your sketch as general as possible. For instance, as you sketch your parallelogram, make sure it’s not almost a rhombus (with four sides that are almost congruent) or almost a rectangle (with four angles close to right angles). If your parallelogram sketch is close to, say, a rectangle, something that’s true for rectangles but not true for all parallelograms (such as congruent diagonals) may look true and thus cause you to mistakenly conclude that it’s a property of parallelograms. Capiche?**

Imagine that you can’t remember the properties of a parallelogram. You could just sketch one (as in the above figure) and run through all things that might be properties. (Note that this parallelogram does not come close to resembling a rectangle of a rhombus.)

The following questions concern the sides of a parallelogram (refer to the preceding figure).

- Do the sides appear to be congruent?Yes, opposite sides look congruent, and that’s a property. But adjacent sides don’t look congruent, and that’s
*not*a property. - Do the sides appear to be parallel?Yes, opposite sides look parallel (and of course, you know this property if you know the definition of a parallelogram).

The following questions explore the angles of a parallelogram (refer to the figure again).

- Do any angles appear to be congruent?Yes, opposite angles look congruent, and that’s a property. (Angles
*A*and*C*appear to be about 45°, and angles*B*and*D*look like about 135°). - Do any angles appear to be supplementary?Yes, consecutive angles (like angles
*A*and*B*) look like they’re supplementary, and that’s a property. (Using parallel lines! angles*A*and*B*are same-side interior angles and are therefore supplementary.) - Do any angles appear to be right angles?Obviously not, and that’s not a property.

The following questions address statements about the diagonals of a parallelogram

- Do the diagonals appear to be congruent?Not even close (in the above figure, one is roughly twice as long as the other, which surprises most people) — not a property.
- Do the diagonals appear to be perpendicular?Not even close; not a property.
- Do the diagonals appear to be bisecting each other?Yes, each one seems to cut the other in half, and that’s a property.
- Do the diagonals appear to be bisecting the angles whose vertices they meet?No.