A parallelogram is a type of quadrilateral with two pairs of parallel sides. The parallelogram is considered a parent figure because several other shapes are parallelograms, but with additional restrictions. These other shapes include the square, rectangle and rhombus. All parallelograms share some traits regarding the length of their sides and measurement of their interior angles.
Angles
Opposite angles of a parallelogram are equal to one another. Since parallelograms are quadrilaterals, the interior angles add up to 360 degrees; any two consecutive angles add up to 180 degrees. The nature of a parallelogram's angles makes it easy to find the measurements of unknown angles. For example, if one angle is 70 degrees, you know that its opposite angle is also 70 degrees and that the angle next to it is 180 minus 70, therefore it equals 110 degrees.
Diagonals
The diagonal of a parallelogram is the distance between any two opposite vertices. Each diagonal of a parallelogram divides the figure into two congruent triangles. The two diagonals of a parallelogram divide each other in half.
Measurements
The area of a parallelogram is equal to its base times its height. You can use any side of the parallelogram as the base when calculating area, but the base and height have to be perpendicular. The sides of a parallelogram are not perpendicular to each other, but you can draw a line that forms a 90-degree angle with the base and extends to the opposite side to represent height. The perimeter, or distance around a parallelogram, is the sum of the lengths of all its sides.
Applications
Since the diagonal of a parallelogram divides the figure equally, the area of a parallelogram is also twice the area of one triangle created by the diagonal. Parallelograms have rotational symmetry at 180 degrees, meaning any parallelogram can be rotated 180 degrees and still look the same.
Variations of Parallelograms
Each of the other shapes that fit the requirements for a parallelogram has its own set of restrictions. The rectangle is a quadrilateral whose opposite sides are parallel and equal; however, all the interior angles of a rectangle have to be 90 degrees. All the sides of a square are equal, and the interior angles are all 90 degrees. All sides of a rhombus are equal, and opposite sides are parallel; opposite angles of a rhombus are also equal.
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