Parallelogram

The name “parallelogram” comes from the Greek phrase “parallelogrammon,” which means “bounded by parallel lines.” As a result, a parallelogram is a quadrilateral with parallel lines dividing it. It’s a form with parallel and equal opposite sides. The three basic types of parallelograms are square, rectangle, and rhombus, each with its own set of characteristics. We will learn about parallelograms, how to calculate their area, and other elements of parallelograms in this part, which will include solved cases.

What is a Parallelogram?

A parallelogram is a type of quadrilateral produced by intersecting lines. A parallelogram’s angle between neighboring sides can vary, but the opposing sides must be parallel to be considered a parallelogram. If the opposing sides of a quadrilateral are parallel and congruent, it is a parallelogram. As a result, a parallelogram is defined as a quadrilateral with parallel and equal sides on both sets of opposing sides. Examine the diagram below, which depicts the three varieties 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

Parallelograms can be divided into various types based on their different properties. There are primarily three types:

  • Rectangle
  • Square
  • Rhombus

Let us study these parallelograms in detail.

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