Parallelogram - Definition, Formulas, Properties and Examples

A quadrilateral with two opposed sides that are parallel and equal in length is referred to as a parallelogram. Hence, a parallelogram has four equal-sized angles, making it a parallelogram.

With a parallelogram, an angle's measurement can be calculated using the following formula: (4 - 2)/2 = 1. According to this equation, the total interior angle of a parallelogram is (4 – 2) 180 degrees, or 360 degrees. We can determine the size of each angle by dividing the total number of degrees by the number of angles in a parallelogram, which is 4. In this instance, each angle of a parallelogram is 90 degrees in length.

It's significant to remember that the length of a parallelogram's sides has no bearing on the measure of an angle within it. This is due to the fact that the amount of rotation necessary to transfer one side of an angle to the other determines the angle's measurement.

In a parallelogram, an angle is defined as being 90 degrees in length. This idea is crucial to comprehend in geometry and has numerous practical uses in fields like building and design.

Parallelogram Definition

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles are additional to the transversal on the same side. The Sum of all the inside angles equals 360 degrees.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The is determined by its base (one of its parallel sides) and height (the distance between its top and bottom). A parallelogram's perimeter is determined by the lengths of its four sides.

The shapes of a square and rectangles share the qualities of a parallelogram.

Angles of a parallelogram

is a two-dimensional flat shape with four angles. The internal angles on either side are equal. The transversal angles on the same side are supplementary, which means they sum to 180 degrees. As a result, a parallelogram's internal angles add up to 360 degrees.

Properties of angles of a parallelogram

A quadrilateral with equal and parallel opposite sides is referred to as a parallelogram. A parallelogram stands apart from other quadrilaterals due to a few unique characteristics. Look at the parallelogram below and compare it to the attributes listed below:

the parallelogram's angles

A parallelogram's opposing angles are congruent (equal). In this case, A Equals C, and D = B.

A parallelogram has angles that sum to 360°. Here, A + B + C + D = 360 degrees.

Each consecutive angle is additional. In this case, A + B = 180°, B + C = 180°, C + D = 180°, and A + D = 180°.

Theorems Concerning a Parallelogram's Angles

Theorems of a parallelogram's angles can be used to help address parallelogram-related issues. The following two significant theorems are listed:

• The opposite angles of a parallelogram are equal.

• Consecutive angles of a parallelogram are supplementary.

Formulas of a parallelogram

Area= Length * breadth

Perimeter= 2 (length + breadth)

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

• The opposite sides are parallel and equal

• The opposite angles are equal

• The consecutive or adjacent 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 the squares of all the sides of a parallelogram is equal to the sum of the squares of its diagonals. It is also called parallelogram law