Originating in the Latin word parallelogrammus, the concept of parallelogram serves to identify a quadrilateral where opposite sides are parallel to each other . This geometric figure it constitutes, therefore, a polygon that is composed of 4 sides where there are two cases of parallel sides.

It is interesting to note that there are different types of parallelograms. The parallelograms of the group of rectangles , for example, are the figures where you can see internal angles of 90º. Within this set are included the square (where all sides have the same length) and the rectangle (where the sides that oppose each other have identical length).

The parallelograms that are considered as non-rectangles On the other hand, they are characterized by having 2 acute interior angles and the others obtuse. This classification includes diamond (whose sides share the same length and also has 2 pairs of identical angles) and at rhomboid (with the opposite sides of identical length and 2 pairs of angles that are also equal to each other).

To calculate the perimeter of the parallelograms it is necessary to add the length of all its sides. This can be done through the following formula: Side A x 2 + Side B x 2 . For example: the perimeter of a rectangular parallelogram that has two opposite sides of 5 centimeters and two opposite sides of 10 centimeters, will be obtained by placing these values ​​in the equation outlined above, which will give us 5 x 2 + 10 x 2 = 30 centimeters.

Another formula for establishing the perimeter of a parallelogram is 2 x (Side A + Side B) . In our example: 2 x (5 + 10) = 30. All these formulas in short, they simplify the process of adding the sides that each parallelogram has. If we perform the operation Side A + Side A + Side B + Side B , the result would be the same (5 + 5 +10 + 10 = 30).

The call parallelogram law, on the other hand, defines that if the lengths are added to the square of each of the four sides of any parallelogram, the result we will obtain will be equivalent to adding the squares of its two diagonals.

With respect to their properties, it is necessary to contemplate them in groups, since, as mentioned above, many forms of different characteristics are considered parallelograms. Some of the common to all are:

* they all have four sides and four vertices, since they belong to the group of quadrilaterals;
* their opposite sides never cross, since they are always parallel;
* the length of the opposite sides is always the same;
* their opposite angles measure the same;
* the sum of two of his vertices, provided they are contiguous, it gives 180 °, that is, they are supplementary;
* the interior angles must add 360 °;
* its area must always be twice that of a triangle constructed from its diagonals;
* every parallelogram is convex;
* its diagonals must bisect each other;
* the point at which its diagonals are bisected is what is considered the center of the parallelogram;
* its center is at the same time its barycenter;
* if you draw a line that crosses its center the area The parallelogram is divided into two identical parts.

On the other hand, the different types of parallelograms can present particular properties, which do not apply to the rest. For example:

* a square parallelogram can give an identical figure if it is rotated in 90 ° sections, which can also be expressed by saying that it has rotation symmetry of order 4;
* those of the rhomboid, rhombus and rectangle type, on the other hand, must be rotated 180 ° to obtain the same result;
* a rhombus has 2 axes of symmetry, which cut it by joining its opposite vertices;
* a rectangle, on the other hand, has 2 axes of reflection symmetry that are perpendicular to its sides;
* The square, finally, has 4 axes of reflection symmetry, which join each pair of opposite vertices and cut through the center vertically and horizontally.