Classifying Quadrilaterals

Any two-dimensional shape with four straight edges is a quadrilateral. There are some special types of quadrilaterals with specific properties that help us to classify quadrilaterals into a variety of groups. The properties that are normally used to classify quadrilaterals include: side lengths, angle measurements, parallel sides, adjacent sides, and diagonals. Some quadrilaterals can be classified in several ways, but they are usually classified as the quadrilateral with the most strict definition. For example, a square meets the criteria to be a rectangle, a parallelogram, a rhombus, a kite, and a trapezoid, but we usually just call it a square. Usually calling a square anything else will tend to confuse students, so it might be best to avoid that discussion until they have a firm grasp on the properties of all quadrilaterals.

The Square

• All four angles must be 90 degrees
• All four sides must be equal in length
• Opposite sides must be parallel
• Diagonals must cross at a 90 degree angle

The Rectangle

• All four angles must be 90 degrees
• Opposite sides must be equal
• Opposite sides must be parallel
• Diagonals may cross at various angles

The Rhombus

• Opposite angles must be equal
• All four sides must be equal in length
• Opposite sides must be parallel
• Diagonals must cross at a 90 degree angle

The Parallelogram

• Opposite angles must be equal
• Opposite sides must be equal in length
• Opposite sides must be parallel
• Diagonals may cross at various angles

The Trapezoid

• Opposite angles may be different
• Opposite sides may be different in length
• One pair of opposite sides must be parallel
• If one pair of opposite sides is equal in length, it is an isosceles trapezoid.
• If there is at least one right angle, it is a right-angled trapezoid.

The Kite

• Opposite angles must be equal
• There must be two pairs of equal adjacent sides
• There is no requirement for parallel sides
• Diagonals must cross at a 90 degree angle

Other Quadrilaterals

There are several other specific quadrilaterals including a dart (a concave quadrilateral), a bowtie (a complex quadrilateral), and several others that are a little beyond the scope of elementary mathematics.

There is no doubt that students who learn the quadrilaterals in this article and can identify them readily, will most likely experience success when it comes to more advanced concepts like finding the area of polygons, circle geometry and algebra. To practice identifying quadrilaterals, check out our Classifying Quadrilaterals worksheet at Math-Drills.com.