Facts about Parallelograms

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On running a search for the most commonly known quadrilaterals, most links that appear on the Google page list Rectangles and squares at the top.
While these two four sided figures own the internet as the most common quadrilaterals, there exists another that wins hands down for being listed as the most often searched quadrilateral.

With two sheared and four parallel sides, this quadrilateral has a mechanism to its name among its various other applications. This quadrilateral is the parallelogram.
Apart from these, the parallelogram also finds its use in a famous English phrase “Think outside the quadrilateral parallelogram”, that means the same as to think out of the box.

Here are a few facts about this shape.

1. What is a parallelogram?
A parallelogram is defined as a four sided figure (quadrilateral) whose opposite sides are parallel to each other.

2. Origin of the word.
The word parallelogram originated in the 16th century from the Latin words ‘Parallelos’ meaning “parallel” and ‘gramme’ meaning “line”.

3. History of Parallelograms.
The concept of parallelograms was first explained by the Greek mathematician, Euclid. It forms an integral part of the Euclidian geometry put forth by him and has been explained in his book on geometry, The Elements.

4. Properties of a parallelogram.
Properties of parallelograms are as follows:
i. Opposite sides of a parallelogram are equal.
ii. Opposite angles of a parallelogram are equal.
iii. Consecutive angles of a parallelogram add up to 180 degrees.
iv. Diagonals of a parallelogram bisect each other.
v. Diagonals of a parallelogram form congruent triangles.

5. Proving that a quadrilateral is a parallelogram.
A quadrilateral is proved to be a parallelogram by testing if all conditions satisfy the properties of parallelograms. The most important test for parallelograms is the diagonal test. A parallelogram when cut by one of its diagonals forms two obtuse triangles and when cut by the other, forms two acute triangles.

6. Area of a parallelogram.
The area of a parallelogram is calculated as twice as that of a triangle.
Area of a triangle = ½*(Base*Height).
Thus, area of a parallelogram = Base x Height.

7. The Rhombus, Rectangle and Square.
Rhombus, Rectangle and Square are all special forms of parallelograms. They may be described as follows:
Rhombus- A parallelogram whose opposite and adjacent sides are equal is called a rhombus.
Rectangle- A parallelogram whose opposite and adjacent angles are equal is called a rectangle.
Square- A parallelogram whose opposite and adjacent sides and angles are equal is called a square.

8. The 3D parallelogram.
A 3D parallelogram is called a Parallelepiped. A parallelepiped is formed by shearing the opposite sides of a rectangle or square.

9. A parallelogram may be classified as a trapezoid.
A trapezoid is defined as a quadrilateral that contains one pair of parallel sides. Parallelograms have two pairs of parallel sides and are thus classified as special types of trapezoids.

10. Formations of parallelograms from equilateral triangles.
On constructing equilateral triangles on either side of a parallelogram, a bigger parallelogram is formed.
On further constructing equilateral triangles inside a parallelogram, another parallelogram equal to the original one drawn is formed.

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