Compare & classify quadrilaterals
In Year 4 (NSW Stage 2, outcome MA2-2DS-01), students compare and classify quadrilaterals, the four-sided shapes: the square, rectangle, rhombus, parallelogram, trapezium and kite.
Students sort quadrilaterals using three features: pairs of parallel sides, equal sides and right angles. They name a quadrilateral from its marked diagram or a description, see what two shapes have in common and how they differ, and learn that one shape can belong to more than one family, so every square is also a rectangle and a rhombus.
Theory
Comparing and classifying quadrilaterals is a Year 4 geometry skill: naming four-sided shapes such as the square, rectangle, rhombus, parallelogram, trapezium and kite. This page shows how to sort them by their parallel sides, equal sides and right angles.
A quadrilateral is any flat, closed shape with four straight sides and four corners. The word "quad" means four. Squares, rectangles, rhombuses, parallelograms, trapeziums and kites are all quadrilaterals.
We tell the special quadrilaterals apart using three tests: how many pairs of parallel sides it has (sides that run the same way and never meet), which sides are equal in length, and how many right angles (square corners) it has.
A square has four equal sides and four right angles. A rectangle has four right angles with opposite sides equal. A rhombus has four equal sides but no right angles. A parallelogram has two pairs of parallel sides. A trapezium has exactly one pair of parallel sides. A kite has two pairs of equal sides that sit next to each other.
Use this table to sort a quadrilateral. Read across each row to see its parallel sides, equal sides and right angles.
| Shape | Pairs of parallel sides | Equal sides | Right angles |
|---|---|---|---|
| Square | 2 | all 4 equal | 4 |
| Rectangle | 2 | opposite sides equal | 4 |
| Rhombus | 2 | all 4 equal | 0 |
| Parallelogram | 2 | opposite sides equal | 0 |
| Trapezium | 1 | none needed | none needed (a right-angled trapezium has 2) |
| Kite | 0 | 2 pairs next to each other | none needed |
Some shapes belong to more than one family. A square has everything a rectangle needs and everything a rhombus needs, and a rhombus and a rectangle both have everything a parallelogram needs.
How to name a quadrilateral
- Count the sides. Check it has four straight sides, so you know it is a quadrilateral.
- Read the marks. Look for tick marks (equal sides), small corner squares (right angles) and arrows (parallel sides).
- Match to a name. Compare the features to the table and choose the best name. If more than one name fits, pick the most special one, like square.
\(4\) right angles \(\to\) a square or a rectangle.
The sides are not all the same length, so it is not a square.
The shape is a rectangle.
All \(4\) sides are equal, so it does fit the rhombus rule.
It also has \(4\) right angles. A shape with \(4\) equal sides and \(4\) right angles is a square.
When more than one name fits, choose the most special one: the best name is square.
A kite has no parallel sides.
A trapezium has exactly \(1\) pair.
A rhombus has \(2\) pairs.
So the trapezium and the rhombus have parallel sides.
A rhombus always has \(2\) pairs of parallel sides (and opposite sides equal).
So yes, every rhombus is a special parallelogram whose four sides are all equal.
Common pitfalls
Frequently asked questions
What is a quadrilateral?
A quadrilateral is a flat, closed shape with four straight sides and four corners. Squares, rectangles, rhombuses, parallelograms, trapeziums and kites are all quadrilaterals.
What is the difference between a rhombus and a parallelogram?
Both have two pairs of parallel sides. A rhombus has all four sides equal, but a parallelogram only needs its opposite sides to be equal.
What is the difference between a rectangle and a parallelogram?
Both have two pairs of parallel sides with opposite sides equal. A rectangle also has four right angles, while a parallelogram has slanted corners. So every rectangle is a parallelogram, but not every parallelogram is a rectangle.
Can a trapezium have a right angle?
Yes. A right-angled trapezium has two square corners on one side. It still has only one pair of parallel sides.
Is a kite a parallelogram?
No. A kite has no parallel sides at all, and a parallelogram needs two pairs of parallel sides.
What makes a shape a kite?
A kite has two pairs of equal sides that sit next to each other, not opposite. It has no parallel sides. A kite you fly in the park is this shape.