In this lesson we will learn what is a parallelogram, how to identify a parallelogram, what are different types of parallelogram and properties associated with them.
Before looking into different types of parallelogram we should first try to understand what is a parallelogram.
What is a Parallelogram ?
In simplest terms a parallelogram is defined as a four-sided plane figure with opposite sides parallel. It is a close bound figure as shown in figure. Parallelogram differs from a
quadrilateral because it has following special properties.
How to identify a parallelogram?
If any one of the following conditions takes place then we can call that quadrilateral a parallelogram:
1. If in a quadrilateral, there are two pairs of parallel sides, then it will be a parallelogram.
2. If in a quadrilateral, two pairs of opposite sides are of the same lengths, then it will be a parallelogram.
3. If in a quadrilateral, two pairs of opposite
angles are same, then it will be a parallelogram.
4. If in a quadrilateral, the diagonals bisect each other, then it will be a parallelogram.
5. If in a quadrilateral, one pair of opposite sides which are parallel and equal in length, then it will be a parallelogram.
Properties of a parallelogram:
The properties associated to a parallelogram which will be true in all types of parallelogram are as follows:
1.
Opposite sides are equal (AB=CD, AD=BC).
2.
Opposite angles are equal (A=C, B=D).
3. Two opposite sides are equal and parallel (AB=CD, AB||CD).
4. Diagonals are divided in their intersection point into two (AO=OC, BO=OD).
Types of parallelogram:
The parallelogram are of following types according to some special properties associated to each one of them.
1. Square :
A square is a special type of parallelogram. The properties associated to a square are:
1. All sides are equal in length.
2. Each angle in a square is 90 degrees.
3. Diagonals of square bisect each other at right angles.
4. The area of square is square of side.
2. Rectangle :
1. Opposite sides are equal in length.
2. Each angle in a rectangle is 90 degrees.
3. The diagonals of rectangle bisect each other at right angles.
4. The area of rectangle is product of length and breadth.
3. Rhombus :
1. All sides are equal in length.
2. No angle is equal to 90 degrees.
3. The diagonals bisect each other and intersect at right angles.
4. The area of a rhombus is product of base and height of the perpendicular.
To learn how to distinguish between different type of parallelogram refer to
link
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