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Parallelogram: Definition of a Parallelogram, Basic Properties of a Parallelogram, Shape of a Parallelogram, Types of Parallelogram
Definition
- A Parallelogram is a two-dimensional shape in sides are parallel to each other.
- In Euclidean geometry, a parallelogram can be defined as a simple quadrilateral with two pairs of parallel sides.
- In other words, we can define a parallelogram as a quadrilateral with two pairs of parallel sides.
Basic Properties of a Parallelogram
- Total number of sides are four.
- Total number of vertices are four.
- Mutually parallel sides are two.
- The opposite angles are congruent.
- Area is equal to the multiplication of base and height.
- Perimeter is twice the sum of adjacent sides length.
- The sum of adjacent angles of a parallelogram is equal to 180°.
- The sum of all the interior angles equals 360°.
In the above figure and
Also, we have and ; and
Since are supplementary and are supplementary,
and
Types of a Parallelogram
Rhomboid
- The opposite pair of sides are parallel.
- The opposite sides of a rhomboid are also congruent.
- The diagonal divides the rhomboid into two congruent triangles.
- The opposite angles of a rhomboid are also congruent.
- The sum of interior angles of a rhomboid is equal to 360°.
- A rhomboid becomes a rhombus if all the sides become equal and therefore a rhombus is always a rhomboid.
Rectangle
- A parallelogram with four angles of equal size (right angles) .
- In a rectangle the diagonals are congruent.
- The opposite sides are equal in a rectangle.
- Each angle in the rectangle is the angle bisector of the opposite angle.
Rhombus
- A parallelogram with four sides of equal length.
- A rhombus is an equilateral quadrilateral.
- An equilateral quadrilateral is one in which all the sides are equal.
- In case of a kite, when all the sides become equal in length the kite becomes a rhombus.
Square
- A parallelogram with four sides of equal length.
- The angles of equal size (right angles) .
- The diagonals are perpendicular bisectors of each other.
- The lengths of the diagonals are equal.
- All such squares in which the diagonals are congruent and bisect the angles are termed as parallelogram.
- Every square is a rectangle and a rhombus.
Area of the Parallelogram
In the given parallelogram b is the base and h is the height and it can be divided into a trapezoid and a right triangle, Also in the second figure a parallelogram has been rearranged into a rectangle.
Therefore, the area of a parallelogram is the same as that of a rectangle with the same base and height
In the above parallelogram the area is
Perimeter of Parallelogram
Perimeter = 2 (a + b) units