Every day the individual is constantly coming across a series of geometric figures that can be viewed at any time. These thousands and thousands of figures can be a notebook, a window, a table, a ball, a door, in short, there is a variety of objects that are drawn by diagonal, straight, oblique lines, among others, that form geometric figures. It is also applicable to other sciences as well as in any field, at least the carpenter, the engineer, the architect, the designer and others, can use these figures and among those disciplines or daily environment we will find some with the shape of a parallelogram.
In the area of mathematics there is a geometric figure that has the shape of a polygon, also called a parallelogram. This is characterized by having four right angles whose opposite sides are parallel, that is to say that their sides have the same diameter and if you add all their angles that are ordered together, they give a total of 180°. In order for a quadrilateral to be formed, it is necessary to draw a pair of diagonals whose central point must coincide.
Its expression derives from the Latin parallelogrammus, whose definition can be expressed as follows: it is a quadrilateral in which the pairs of opposite sides are parallel and retain the same diameter.
Characteristics and properties of the parallelogram.
A wide variety of characteristics can be visualized in a parallelogram such as:
- All its interior angles are less than 180 degrees and its interiors are diagonals.
- Its two pairs of sides will always be parallel and they will also be.
- Its sides that are opposite are also even.
- A point is started at the center of a parallelogram when drawing the diagonals.
- Their opposite sides are never joined.
- The sum of all its internal sides will always be 360 degrees.
- The parallelogram has both vertex and sides four quantities.
- Their opposite angles have equal measures.
Among its most common properties that characterize it we have the following:
- The midpoints or central points are cut by the two diagonals.
- Its two opposite angles will always be equal.
- Its two angles always complement each other and their sum is 180 degrees.
- Opposite sides that are even are equal.
Classification of types of parallelograms.
It is interesting to know how many kinds of figures there are in geometry, and among them we have:
- Square, its angles are right and its sides are equal and both have four well symmetrical axes.
- Rectangle, its opposite sides are of equal length and its four angles are right and have two axes that are perpendicular.
- Rhombus, its four sides have the same length and their adjacent angles are different, having two axes that are diagonal.
- Rhomboid or also called non-regular parallelogram, its four sides are not equal and none of its angles are right, here logically it does not have any axis with symmetry. Here this formula is fulfilled: a + b=180 degrees.
- Cube, is composed of six faces and each face is square in shape.
- Polygon is a figure that is presented in a two-dimensional form with lines that are straight lines connected to each other in a very closed way.
- Trapezoid, is a geometric figure that is made up of four sides and they are not parallel to each other.
- Trapezoid, is a figure made up of four sides and two of them are parallel.
Law and existing elements in a parallelogram.
There is a law that strengthens the geometry that serves to relate all the sides of a quadrilateral with its diagonals, applying a formula expressed in a mathematical way to get its length as such, this is the following:
(AB)^2+(BC)^2+(CD)^2+(DA)^2 =(AC)^2+(BD)^2. Whose vertices are: A, B, C, D.
This law establishes that the sum of the lengths or measures of the four sides of the square is proportional to the sum of the lengths or measures of the squares of two diagonals.
Among the most outstanding elements that make up this geometric figure are:
- Sides, make up four sides that in turn are equal and very parallel (a and b).
- Angles are not consecutive, although their internal angles are equal.
- Diagonals, this element puts into practice the parallelogram law, in which if they are perpendicular they form a rhombus and if they are equal they form a rectangle.
There are other types of formula that help to find the perimeter of a quadrilateral and they are the following: here only the lengths of each side of the polygon are added and mathematically speaking it is done with these formulas:
Side A x 2 + Side B x 2 and another formula 2 x (Side A + Side B) is better explained through an example:
The perimeter of a rectangle whose sides measure 5 centimeters and its two opposite sides are 10 centimeters long, its result will be the following: 5 x 2 + 10 x 2 = 30 centimeters or using this other one: 2 x (5 + 10)=30 centimeters.