6 Properties of Parallelograms: A Comprehensive Guide

Parallelograms are four-sided shapes that feature two sets of parallel lines. These shapes are present in almost every day object we encounter, from the windowpanes in our homes to the tiles on the floor. Understanding the properties of parallelograms is essential for anyone looking to gain a better understanding of geometry, especially for those studying for the GRE. This article will explore six properties of parallelograms, including their angles, sides, diagonals, and more.

1. Parallel Sides

One of the defining characteristics of a parallelogram is that it has two sets of parallel sides. This means that the opposite sides of the parallelogram are parallel and of equal length. This is essential for the other properties of the parallelogram to hold true. The parallel sides of a parallelogram are what make it different from other four-sided shapes such as a square or rectangle.

2. Opposite Sides are Equal

Because a parallelogram has two sets of parallel sides, the opposite sides are equal in length. This means that the length of one side will be equal to the length of its opposite side. This is true for any parallelogram regardless of its size or shape. This is an important property to remember when calculating the area of a parallelogram.

3. Opposite Angles are Equal

Due to the fact that a parallelogram has two sets of parallel sides, it follows that the opposite angles of a parallelogram are also equal. This means that the angles of a parallelogram will always add up to 180 degrees. For example, if one angle of a parallelogram is 30 degrees, then its opposite angle must also be 30 degrees.

4. Diagonals Bisect Each Other

All parallelograms have two diagonals that intersect at their midpoint. This means that if you draw a line through the midpoint of one diagonal, it will bisect the other diagonal in half. This property is useful when trying to calculate the area of a parallelogram, as it can help you divide the shape into two triangles, each of which can then be used to calculate the area of the parallelogram.

5. Adjacent Angles are Supplementary

The adjacent angles of a parallelogram are supplementary angles. This means that the sum of the adjacent angles is equal to 180 degrees. This property is often useful when trying to calculate the angles of a parallelogram. For example, if one adjacent angle of a parallelogram is 45 degrees, then the other adjacent angle must be 135 degrees.

6. All Parallelograms are Quadrilaterals

A parallelogram is a type of quadrilateral, meaning it is a four-sided shape. All of the properties of a parallelogram apply to any quadrilateral, so it is important to remember that any parallelogram will also follow the properties of a quadrilateral. This is important to remember when calculating the area or perimeter of a parallelogram.

Parallelograms are four-sided shapes that feature two sets of parallel lines. This article has explored six properties of parallelograms, including their angles, sides, diagonals, and more. Understanding the properties of parallelograms is essential for anyone looking to gain a better understanding of geometry. It is also important to note that all of the properties of a parallelogram also apply to any quadrilateral.