A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to 180 degrees. In geometry, you must have learned about many 2D shapes and sizes such as circle, square, rectangle, rhombus, etc. All of these shapes have a different set of properties. Also, the area and perimeter formulas of these shapes vary from each other and are used to solve many problems.
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.
A three-dimensional shape that has its faces in parallelogram shape, is called a parallelepiped. The area of parallelogram depends on the base (one of its parallel sides) and height (altitude drawn from top to bottom) of it. The perimeter of a parallelogram depends on the length of its four sides.
A square and a rectangle are two shapes which have similar properties of a parallelogram.
Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it is a rhombus.
Facts:
- Number of sides = 4
- Number of vertices = 4
- Mutually Parallel sides = 2 (in pair)
- Area = Base x Height
- Perimeter = 2 (Sum of adjacent sides length)
- Type of polygon = Quadrilateral
Special Parallelograms
Square and Rectangle: A square and a rectangle are two shapes which have similar properties of a parallelogram. Both have their opposite sides equal and parallel to each other. Diagonals of both shapes bisect each other.
Rhombus: If all the sides of a parallelogram are congruent or equal to each other, then it is a rhombus.
Rhomboid: A special case of a parallelogram that has its opposite sides parallel to each other but adjacent sides are of unequal lengths. Also, the angles are equal to 90 degrees.
Trapezium: If there is one parallel side and the other two sides are non-parallel, then it is a trapezium.
Angles of Parallelogram
A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.
Properties of Parallelogram
If a quadrilateral has a pair of parallel opposite sides, then it’s a special polygon called Parallelogram. The properties of a parallelogram are as follows:
- The opposite sides are parallel and congruent
- The opposite angles are congruent
- The consecutive angles are supplementary
- If any one of the angles is a right angle, then all the other angles will be at right angle
- The two diagonals bisect each other
- Each diagonal bisects the parallelogram into two congruent triangles
- The Sum of square of all the sides of parallelogram is equal to the sum of square of its diagonals. It is also called parallelogram law