State and Explain 5 Properties of a Parallelogram

A parallelogram is a geometrical shape with sides that are parallel to each other in two dimensions. It’s a four-sided polygon (also named quadrilateral) with two parallel sides that are the same length. A parallelogram’s interior opposite angles are also similar in size. The sum of a parallelogram’s adjacent angles is 180 degrees. A quadrilateral with two pairs of parallel sides is known as a parallelogram. The lengths of the opposite sides of a parallelogram are identical, as are the measures of the opposite angles. Additionally, the interior angles on the same transversal side are supplementary. 360 degrees is the sum of all angles. A square and a rectangle are two shapes that have parallelogram-like properties.

Fun Facts:

  • Number of sides in a parallelogram = 4
  • Number of vertices in a parallelogram = 4
  • Mutually Parallel sides in a parallelogram= 2 (in pair)
  • Area = Base x Height
  • Perimeter = 2 (Sum of adjacent sides length)
  • Type of polygon = Quadrilateral

The Shape of a Parallelogram?

A parallelogram is a shape of two dimensions. It consists of four sides, with two pairs of parallel sides. In addition, the lengths of the parallel sides are similar.

The form is not a parallelogram if the length of the parallel sides is not identical in measurement. Similarly, the interior angles of a parallelogram’s opposite sides should always be equal. It isn’t a parallelogram otherwise.

Special Parallelogram:

Square and Rectangle: A square and a rectangle are two shapes that have parallelogram-like properties. Both have opposite sides that are equal and parallel to one another. Both shapes’ diagonals bisect each other.

  • Rhombus: A rhombus is formed when all of the sides of a parallelogram are congruent or equivalent.
  • Rhomboid: A parallelogram with opposite sides that are parallel to each other but opposing sides that are unequal in length. In addition, the angles are all 90 degrees.
  • Trapezium: A trapezium is described as a shape with one parallel side and two non-parallel sides.

Angles of a Parallelogram:

A parallelogram is a flat two-dimensional shape with four angles. The interior angles on both sides are the same. The transversal angles on the same side are supplementary, meaning they add up to 180 degrees. As a result, the number of a parallelogram’s interior angles is 360 degrees.

Types of Parallelogram

There are mainly four comprehensive types of Parallelogram, depending on diverse factors and their properties. The factors which distinguish between all of these various types of a parallelogram are angles, sides, etc.

In a parallelogram, let us take PQRS. Here if PQ = QR = RS = SP is the given equal sides, then it is named as a rhombus. All the properties are similar for a rhombus as for a parallelogram. The other two essential types of a parallelogram are stated below:

  • Rectangle
    • Square

The Area and Perimeter of a Parallelogram:

Area:

It is the region or area covered by it in a two-dimensional plane.

Formula:

Area = Base x Height

Perimeter

It is the total length of the sides of a parallelogram. It is equal to the sum of all four boundaries.

Formula= 2(a+b)

The 5 Properties of a Parallelogram

If a quadrilateral or shape includes a pair of parallel opposite sides, then it is a special polygon called Parallelogram. The primary properties of parallelogram are as follows:

  1. The opposite sides are parallel and congruent in a parallelogram
  2. The consecutive angles are supplementary in a parallelogram
  3. If anyone of the angles is proved to be a right angle, then all the other angles will be the right angle in a parallelogram
  4. Every diagonal bisects the parallelogram into two different congruent triangles
  5. The sum of all the existing squares of all the sides of a parallelogram is equal to the total sum of squares of its diagonals. It is also named the parallelogram law.

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