Which of the following are characteristics of parallelograms select all that apply?

One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel.

There are six important properties of parallelograms to know:

1. Opposite sides are congruent (AB = DC).
2. Opposite angels are congruent (D = B).
3. Consecutive angles are supplementary (A + D = 180°).
4. If one angle is right, then all angles are right.
5. The diagonals of a parallelogram bisect each other.
6. Each diagonal of a parallelogram separates it into two congruent triangles.
   

$$\triangle ACD\cong \triangle ABC$$

If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi.

If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid. The parallel sides are called bases while the nonparallel sides are called legs. If the legs are congruent we have what is called an isosceles trapezoid.

In an isosceles trapezoid the diagonals are always congruent. The median of a trapezoid is parallel to the bases and is one-half of the sum of measures of the bases.

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.

  Which of the following is a characteristics of all parallelograms?

  Properties of Parallelogram The opposite angles are equal. The consecutive or adjacent angles are supplementary. If any one of the angles is a right angle, then all the other angles will be at right angle. The two diagonals bisect each other.

  What are the 7 properties of a parallelogram?

  Properties of Parallelograms Explained.

  Opposite sides are parallel. ... .

  Opposite sides are congruent. ... .

  Opposite angles are congruent. ... .

  Same-Side interior angles (consecutive angles) are supplementary. ... .

  Each diagonal of a parallelogram separates it into two congruent triangles. ... .

  The diagonals of a parallelogram bisect each other..

  Which of the following are properties of all parallelograms select all that apply?

  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..

  What are the 4 theorems of a parallelogram?

  Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. HSG-SRT.