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Parallelogram

The term ‘parallelogram’ was derived from the Greek word ‘parallelogrammon’ which stands for “bounded by parallel lines”. Hence, a parallelogram is a quadrilateral that is bounded by parallel lines. It is a shape in which the opposite sides are parallel and equal. Parallelograms are classified into three main types: square, rectangle, and rhombus, and each of them has its own unique properties. In this section, we will learn about a parallelogram, how to find the area of a parallelogram and other aspects related to a parallelogram along with the solved examples.

What is a Parallelogram?

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent. Hence, a parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal. Observe the following figure which shows the three types of parallelograms:

Properties of a Parallelogram

There are some basic properties that help us to identify a parallelogram. Observe the following parallelogram PQTR to relate to its properties given below.

We can identify and distinguish a parallelogram with the help of the following properties:

• The opposites sides of a parallelogram are parallel. Here, PQ ‖ RT and PR ‖ QT.
• The opposite sides of a parallelogram are equal. Here, PQ = RT and PR = QT
• The opposite angles of a parallelogram are equal. Here, ∠P = ∠T and ∠Q = ∠R
• The diagonals of a parallelogram bisect each other. Here, RE = EQ and PE = ET
• Same-side interior angles supplement each other. Here, ∠PRT + ∠RTQ = 180^∘, ∠RTQ + ∠TQP = 180^∘, ∠TQP + ∠QPR = 180^∘, ∠QPR + ∠PRT = 180^∘
• The diagonals divide the parallelogram into two congruent triangles. Here, ΔRPQ is congruent to ΔQTR, and ΔRPT is congruent to ΔQTP

Types of Parallelogram

A parallelogram can be divided into various types depending upon the different properties. It is mainly divided into three special types:

• Rectangle
• Square
• Rhombus