What is a Parallelogram?

Definition and Characteristics of Parallelograms

• A parallelogram is a geometric shape with four sides, four corners, and four angles.
• It has two sets of parallel lines, with either the same length for every side or two different side lengths (one length for each pair of parallel lines).
• Parallelograms will never have more than two side lengths, or they wouldn't be considered a parallelogram.

Types of Parallelogram Shapes

• Squares: four sides of equal length, four 90° angles (or four right angles), and two sets of parallel lines.
• Rectangles: four sides, four corners, and four angles; all angles are right angles, but not all sides are equal length.
• Rhombuses: four sides of equal length, but no right angles; angles are acute and obtuse, each directly across from each other.
• Rhomboids: four sides, but not all sides are equal length; they have two acute and two obtuse angles opposite from each other.

Properties of Parallelograms

• Quadrilateral: four sides
• Parallel sides: two sets of parallel lines opposite from one another
• Bisecting lines: lines drawn diagonally from each corner of a parallelogram will create bisecting lines that intersect halfway from each line
• Equal side length: at least one pair of sides of equal length
• Congruent triangles: two congruent triangles are formed when a single line is drawn diagonally from one corner to another on a parallelogram
• Opposite but equal angles: angles opposite from each other in a parallelogram will have the same measure
• Opposite but equal lines: parallelograms always have sides with the same length (congruent) as the side opposite from them

Calculating the Area of a Parallelogram

• The area of a parallelogram can be determined by multiplying the base by the height of the shape (A = B x H)
• The area of a rectangle, for example, can be calculated by multiplying the base and height (e.g., A = 4cm x 2cm = 6)