Wednesday, July 11, 2012

Quadrilaterals the four sided polygons

In geometry, we learn about Quadrilaterals. What is a Quadrilateral is the question which arises when we read this word. Let us break the word into two parts, Quadri- lateral, Quadri means four and lateral means straight sides. Quadrilateral put together means four sided figure or polygon. Next question that arises in our mind is What shape is a Quadrilateral or what shapes are Quadrilaterals, a four sided figure or polygon can be a rectangle or a square or a rhombus, we have different four sided shapes. From this, we can conclude that any four sided figure is a Quadrilateral whose sides are straight and the figure is two dimensional. The different types of four sided two dimension figures which are included in the list of quadrilaterals are, Parallelogram, Rectangle, Rhombus, Square, Trapezoid and Kite.
Quadrilaterals family

Let us take a quick look at Quadrilateral Properties.
All quadrilaterals have four sides (straight edges)
All quadrilaterals have four corners or vertices
The sum of the interior angles in a Quadrilateral is equal to 360 degrees
Let us now learn the properties of each type of quadrilateral.
Rectangle: A rectangle is a quadrilateral in which every angle is a right angle and opposite sides are parallel and are of equal length
Square: A square has equal sides and equal angles. Each angle is a right angle. Opposite sides are parallel and equal
Rhombus: A Rhombus is a four sided figure in which all sides are of equal length. Opposite sides are parallel and opposite sides are equal. One more interesting property of a rhombus is that the diagonals of a rhombus bisect each other at right angles
Parallelogram: As the name suggests, in a parallelogram opposite sides are parallel and are equal in length. All the opposite angles are equal
Trapezoid: In a trapezoid one pair of sides are parallel. When the sides that are not parallel are equal in length and both angles coming from the parallel sides are equal, they are called Isosceles trapezoid. A quadrilateral with no parallel sides is the trapezium
Kite: Kite has two pairs of sides. Each pair of adjacent sides are equal in length. The angles are equal where the pairs meet. One diagonal bisects the other and they meet at right angles.
 Square is the only regular quadrilateral, all other are irregular quadrilaterals!

While learning about Quadrilaterals in geometry, you might have come across Cyclic Quadrilaterals;
A quadrilateral in which a circle can be circumscribed in such a way that it touches all the four vertices of the polygon is called a Cyclic Quadrilateral. It is something like a quadrilateral inside a circle where the circle passes through all the vertices. In cyclic quadrilaterals the sum of the opposite angles are supplementary.

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