A parallelogram is one of the types of quadrilaterals. A quadrilateral is a closed geometric shape which has 4 vertices, 4 sides and hence 4 angles that lie on the same plane. Sum of the interior angles of a quadrilateral measures 3600. A quadrilateral is a type of a polygon. There are various kinds of quadrilateral embracing trapezoids, parallelograms and kites. A parallelogram is one of the types of quadrilateral in which opposite sides are equal and parallel and opposite angles are equal.
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Let us consider the parallelogram ABCD represented in the above figure to understand the properties of a parallelogram in a better manner. The properties of a parallelogram are listed below.
Opposites sides of a parallelogram are parallel and congruent.
i.e. AB || CD and AC || BD. Also AB = CD and AC = BD
Opposite angles of a parallelogram are congruent.
∠ABC ⩭ ∠ADC and ∠BAD ⩭ ∠BCD
Diagonals of a parallelogram bisect each other.
i.e. AC bisects BD and BD bisects AC.
Sum of any two interior adjacent angles of a parallelogram is a straight angle (i.e. it measures 1800).
If one of the interior angles of a parallelogram is a right angle, then all the interior angles are right angles.
The diagonal of a parallelogram divides the parallelogram into two congruent triangles.
i.e. If the diagonal AC is drawn for the parallelogram ABCD shown in the above figure, the diagonal divides the parallelogram into two triangles: ΔABC and ΔADC such that ΔABC ⩭ ΔADC
The Perimeter of a Parallelogram
The perimeter of a parallelogram is the measure of all sides of a parallelogram. A parallelogram is a two dimensional geometric shape. The two measurable dimensions are length and width. Since opposite sides of a parallelogram are congruent, its perimeter can be written as the sum of all the four sides in terms of length and width as:
The Perimeter of a Parallelogram = 2 (L + B)
In the above equation, ‘L’ is the length and ‘B’ is the breadth or width of the parallelogram.
Area of Parallelogram Formula
A deeper analysis of the parallelogram properties reveal that the parallelograms are made of two congruent triangles. (i.e. the diagonal of a parallelogram divides it into two congruent triangles.) Since the triangles are congruent, they have the same area. The area of a triangle is measured as half of the product of its base and height. Since the parallelogram has 2 triangles, its area is twice the area of the triangle. Therefore, the area of a parallelogram formula is equal to the product of its base and height.
Area of Parallelogram = Base x Height
1. Find the area of a parallelogram whose base is 5 cm and height is 3 cm.
Given: Length of the parallelogram / Base of the parallelogram (B) = 5 cm
Height of the parallelogram (H) = 3 cm
Area of parallelogram formula is given as:
Area = B x H
Area = 5 x 3
Area = 15 cm2
2. Determine the perimeter of a quadrilateral whose sides measure 5 cm, 4 cm, 5 cm and 4 cm taken in an order. Identify whether the given quadrilateral is a parallelogram or not. Justify your answer.
Perimeter of a quadrilateral is the sum of all the 4 sides of the quadrilateral. So,
Perimeter = 5 + 4 + 5 + 4 = 18 cm.
The given quadrilateral is a parallelogram because its opposite sides are found to be equal. If the opposite sides are equal, obviously they will be parallel too.
One of the most important learning outcomes of understanding the concept of parallelogram properties is that the student should be able to identify whether the given quadrilateral is a parallelogram or not.
Check whether the following quadrilaterals are parallelograms or not. Justify your answer.
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All parallelograms are quadrilaterals and all quadrilaterals are not parallelograms.
All rectangles and squares will have the properties of parallelograms whereas all the parallelograms may not be squares or rectangles.
Square is the only example of a regular quadrilateral.
Parallelogram is a two dimensional shape and hence its volume cannot be determined.
1. What are Quadrilaterals? Mention its Types and Properties.
A quadrilateral is a four sided closed geometric shape. It has only two dimensions namely length and width. Quadrilaterals are plane geometric shapes. The different types of quadrilaterals include parallelograms, trapezoid and kite. The different types of parallelograms include rhombus and rectangles. Square is a special type of rectangle. The properties of quadrilaterals are:
All the quadrilaterals have 4 vertices, 4 sides and 4 angles.
Sum of all the four interior angles of a quadrilateral is 3600.
2. What are different Kinds of Parallelograms?
Parallelograms are the four sided closed plane geometric shapes in which the opposite sides are equal and parallel. The two special kinds of parallelogram are:
Rhombus is a parallelogram in which all the sides are congruent and opposite angles are equal.
A parallelogram can be considered as a rectangle if and only if one of the interior angles of the parallelogram is a right angle. (It is very important to note that if one of the interior angles is 900, then all the 4 interior angles also measure 900)
A square is a special type of a rectangle in which all the sides are congruent.