Classify quadrilaterals by properties
Theory
A quadrilateral is named by its sides and angles. Read the tick marks, right-angle marks and parallel-side arrows, then give the most exact name. The four angles always add to \(360^\circ\).
A quadrilateral is a shape with four straight sides and four angles. Special names describe the extra properties a quadrilateral has.
A square has four equal sides and four right angles. A rectangle has opposite sides equal and four right angles. A rhombus has four equal sides but no right angles.
A parallelogram has both pairs of opposite sides equal and parallel. A trapezium has exactly one pair of parallel sides.
Always give the most exact name — the one that uses every property the shape has. The four angles add to \(360^\circ\).
Read the marks, then match them to the most exact name.
| Shape | Equal sides | Right angles |
|---|---|---|
| Square | all four | four |
| Rectangle | opposite pairs | four |
| Rhombus | all four | none |
| Parallelogram | opposite pairs | none |
| Trapezium | usually none | none |
How to name a quadrilateral
- Check the sides. Are all four equal, or only opposite pairs, or none?
- Check the angles. Are there four right angles, or none?
- Choose the most exact name that fits every property the shape has.
Equal sides and right angles means it is a square.
Right angles with opposite sides equal means it is a rectangle.
| \(360^\circ - 90^\circ - 90^\circ - 100^\circ\) | \(=\) | \(80^\circ\) |
One pair of parallel sides means it is a trapezium.
Common pitfalls
Frequently asked questions
What is the difference between a square and a rhombus?
Both have four equal sides, but a square also has four right angles. A rhombus has no right angles, so its corners are slanted.
What is the most exact name?
It is the name that uses every property the shape has. A shape with four equal sides and four right angles is best called a square, not just a rectangle.
Do the angles of a quadrilateral add to 360 degrees?
Yes. Any quadrilateral can be split into two triangles, and each triangle has angles adding to \(180^\circ\), giving \(360^\circ\) in total.
What is a trapezium?
A trapezium is a quadrilateral with exactly one pair of parallel sides. Its other two sides are not parallel.
Is a square a rectangle?
Yes. A square has everything a rectangle needs — opposite sides equal and four right angles — plus all four sides equal, so it is a special rectangle.