Parallelogram

A parallelogram is a type of geometric shape that only exists in two dimensions and has sides that are perpendicular to one another. It is a sort of polygon that has four sides and is also called a quadrilateral, and the lengths of the pair of sides that are parallel to each other are the same. A parallelogram has adjacent angles that add up to a total of 180 degrees when added together. You must have learnt about a variety of 2D shapes and sizes in geometry, such as circles, squares, rectangles, rhombuses, and other similar shapes. These many forms each have their own unique set of characteristics. In addition, the area and perimeter formulas for each of these forms are different from one another and can be applied to the solution of a wide variety of issues. 

Parallelogram definition: 

A quadrilateral that has two pairs of sides that are parallel to one another is called a parallelogram. The lengths of the opposite sides of a parallelogram are equal to one another, and the opposite angles have the same degree of measurement. Additionally, the interior angles that are on the same side of the transversal are considered to be supplementary. The total amount of the internal angles adds up to a full 360 degrees.

A parallelepiped is a term used to describe a three-dimensional shape that has its faces in the shape of a parallelogram. The area of a parallelogram is determined by both its base, which is one of its parallel sides, and its height, which is the elevation measured from the top to the bottom. The length of each of a parallelogram’s sides determines the length of the shape’s perimeter.

Both a square and a rectangle are examples of shapes that share many of the same characteristics as a parallelogram.

A rhombus is defined as a parallelogram in which all of the sides are congruent with one another or are equal to one another.

A trapezium can be identified by its having one parallel side and two other sides that are not parallel to each other. 

In the figure above, ABCD is a parallelogram, where AB || CD and AD || BC. 

Also, AB = CD and AD = BC

And, ∠A = ∠C & ∠B = ∠D 

In addition, A and D are considered additional angles because they are located on the same side of the transversal as the other inner angles. In the same vein, ∠B and ∠C are considered to be supplementary angles. 

Therefore,

∠A + ∠D = 180

∠B + ∠C = 180 

Shape of parallelogram: 

A parallelogram is a shape that only exists in two dimensions. It possesses a total of four sides, two pairs of which are parallel to one another. Additionally, the lengths of the parallel sides are identical. The form in question is not a parallelogram if the lengths of the sides that run parallel to one another do not measure the same. In a similar fashion, both of the parallelogram’s inner angles that are opposite one another should always be equal. In such a case, we cannot call it a parallelogram. 

Properties of parallelogram: 

A unique kind of polygon known as a parallelogram is formed when a quadrilateral has a pair of parallel opposite sides. The following is a list of the characteristics of a parallelogram:

1. The opposite sides are parallel and congruent

2. The angles on opposite sides are identical.

3. The angles that follow one another are complementary.

4. In the event that even one of the angles is a right angle, then the remaining angles will also be right angles.

5. Both diagonals meet and cut each other in half.

6. Each diagonal cuts the parallelogram in half, creating two triangles that are congruent with one another.

7. The parallelogram has a property where the sum of the squares of all of its sides is equal to the sum of the squares of its diagonals. It is also known as the law of the parallelogram. 

Types of parallelogram: 

Because of the many different considerations, parallelograms may generally be broken down into four distinct categories. Angles, sides, and other characteristics such as these are what set each of these distinct parallelogram variations apart from one another. 

1. In a parallelogram, say PQRS 

• If PQ = QR = RS = SP are the equal sides, then it’s a rhombus. All the properties are the same for rhombus as for parallelogram.

2. The other two special types of a parallelogram are:

• Rectangle

• Square 

Angles of parallelogram: 

A parallelogram is a type of two-dimensional form that is flat and has four angles. Equal treatment is accorded to the opposing inner angles. The angles that are located on the same side of the transversal are complementary, which indicates that their sum is equal to 180 degrees. Therefore, the total amount of angles that are contained within a parallelogram is equal to 360 degrees. 

Special parallelograms: 

Square and rectangle: 

Both a square and a rectangle are examples of shapes that share many of the same characteristics as a parallelogram. Both of their opposing sides are of the same length and run parallel to one another. Both shapes can be cut in half along their respective diagonals. 

Rhombus: 

A rhombus is defined as a parallelogram in which all of the sides are congruent with one another or are equal to one another.

Rhomboid: 

A rhomboid is a specific example of a parallelogram in which the sides that are perpendicular to each other are also parallel to the sides that are adjacent to them, but the lengths of the sides that are perpendicular to each other differ. In addition, each angle adds up to exactly 90 degrees.

Trapezium: 

A shape is said to be a trapezium if it has one side that is parallel to itself and two other sides that are not parallel to one another. 

Conclusion: 

A parallelogram has four sides that are perpendicular to one another. Every one of the two sets of opposing sides has the same length and is aligned parallel to one another. The parallelogram, with its singular set of features, has found widespread use in industrial settings for the purpose of correctly transmitting mechanical motion from one location to another.