Parallelogram
A special type of polygons is known as a parallelogram . This is a quadrilateral where both pairs of opposite sides are parallel . The word has its origin in the Latin word parallelogrammus , and this concept helps us to identify a quadrilateral in which the opposite sides are parallel to each other. This geometric figure constitutes is then formed by a polygon that is made up of 4 sides where there are two cases of parallel sides .
What is a parallelogram?
It is a polygon that is formed by four sides and that is characterized because its opposite sides are always parallel to each other or, in other words, they are located at the same distance from each other.
- Characteristics of the parallelogram
- Properties
- Classification
- Elements
- Parallelogram law
- Height
- Diagonals
- Area
- Perimeter
- Angles
- Parallelogram method
- Examples
Characteristics of the parallelogram
The main characteristics that we can observe in a parallelogram are the following:
- It will always have two pairs of sides that are parallel .
- Besides having a pair of sides that are parallel they are also equal .
- Opposite sides are equal to pairs .
- The diagonals intersect at one point , in the middle or center of the parallelogram.
- Their opposite sides never meet.
- The sum of all interior angles will always be 360 degrees .
- Angles that are opposite have equal measure.
- All parallelograms are convex .
- Each parallelogram has four sides and an equal number of vertices .
Properties
The properties that characterize parallelograms are the following:
- The pairs of opposite sides that the parallelogram has will always be equal .
- The pairs of angles that are opposite are equal .
- Every two contiguous angles are supplementary and add up to a total of 180.
- Your two diagonals will always intersect at their midpoints .
Classification
It is important to know that squares , rectangles , rhombuses, trapezoid, trapezoid, polygon, cube and rhomboids are parallelograms, and their main characteristics are the following:
- Square : its four sides are equal and its four angles are right.
- Rectangle : its four angles are right.
- Rhombus : all four sides are equal, but it has two different angles two by two, for this reason, the adjacent angles will be different and each of its angles is equal to the adjacent angle.
- Rhomboid : it has its four sides that are not equal and there is no right angle in them. It is also known as a non-regular parallelogram .
- Cube : it is a body made up of six faces and each of them is square.
- Polygon : it is a two-dimensional figure that has straight lines that connect in a closed way.
- Trapezoid : geometric figure with four sides that are not parallel.
- Trapezoids : a four-sided geometric figure in which two sides are parallel .
Elements
Parallelograms have three different elements that make them up, these are:
- Sides : they have four sides , being equal and parallel two by two (a and b).
- Angles : the interior angles that parallelograms have are equal to two by two, the non-consecutive angles (α and β) being equal .
- Diagonals : if the diagonals (D1 and D2) are perpendicular , the parallelogram will be a square or a rhombus . If the diagonals are equal , it is a square or a rectangle . These two diagonals can be calculated using the parallelogram law.
Parallelogram law
There is a geometric law that aims to relate the sides of a parallelogram with its diagonals, this is known as the parallelogram law. The law tells us that the sum of the squares of the lengths of the four sides of any parallelogram will always be equal to the sum of the squares of the lengths of the two diagonals. It can be represented by the following formula:
(AB) 2 + (BC) 2 + (CD) 2 + (DA) 2 = (AC) 2 + (BD) 2
In which A, B, C, and D are the vertices of the parallelogram.
Height
Height is represented by the letter h and is calculated by dividing the area by the base of the parallelogram.
h = A / b
Diagonals
A diagonal is a segment of straight connecting the interior vertex having a geometric shape with the apex located opposite and is not consecutive to it. In the parallelograms there is a theorem that says that if a quadrilateral is a parallelogram, then the diagonals are bisect one another and that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Area
The area of a parallelogram is the product of multiplying the base times the height . The base is any of its sides and the height is the distance between the base and its parallel side . The formula is as follows:
A = b * h
Where b is the base and h is the height.
Perimeter
The Perimeter, represented by the letter p , can be calculated as the sum of its four sides . Thinking that its opposite sides are equal, we can indicate the perimeter with the following formula: p = 2 a + 2 b
Being a and b the length of two non-consecutive sides of the parallelogram, or taking a common factor we would have: p = 2 (a + b)
Angles
The interior angles that a parallelogram has are equivalent to the sum of the angles of the two triangles that are inside. The sum of these interior angles must be 306 °.
Parallelogram method
This method is a very simple procedure that allows us to find the sum of two vectors . The first step is to draw both vectors, a and b to scale, with a common application point . The second step is to complete a parallelogram by drawing two segments that are parallel to them.
The vector sum that results from the operation a + b will be the diagonal of the parallelogram.
Examples
Some examples of parallelograms are:
- Straight Trapezius
- Scalene Trapezoid
- Trapezium isosceles
- Squares
- Rectangle
- Diamond
