What are quadrilaterals?
Quadrilaterals are shapes that have four straight sides and four angles. All quadrilaterals are closed shapes, meaning their sides connect without gaps.
- A square
- A rectangle
- A rhombus
- A trapezoid
All quadrilaterals share two basic traits: four sides and four angles. Other attributes help us sort them into different types.
Understanding sides and angles
Quadrilaterals can be described by their sides (the lengths and whether any are parallel) and their angles (right angles or angles of different sizes).
- A rectangle has four right angles.
- A rhombus has four equal sides.
- A trapezoid has exactly one pair of parallel sides.
Parallel sides stay the same distance apart and never meet, even if they are extended.
Common quadrilaterals and their attributes
Each type of quadrilateral has special attributes. These attributes help us classify and compare shapes.
- Square — four equal sides and four right angles
- Rectangle — opposite sides are equal and four right angles
- Rhombus — four equal sides and opposite angles are equal
- Parallelogram — opposite sides are parallel and equal in length
- Trapezoid — exactly one pair of parallel sides
- Kite — two pairs of adjacent sides that are equal
Some quadrilaterals can belong to more than one category. For example, every square is also a rectangle because it has four right angles.
Comparing quadrilaterals
We compare quadrilaterals by looking at their sides, angles, and pairs of parallel lines.
- A square and a rhombus both have four equal sides, but only the square has four right angles.
- A rectangle and a parallelogram both have opposite sides that are parallel, but only the rectangle has four right angles.
- A trapezoid has just one pair of parallel sides, unlike a parallelogram, which has two pairs.
Looking at what shapes have in common helps you understand how they are related. Looking at how they differ helps you name each shape correctly.
Using attributes to classify shapes
When you classify a quadrilateral, you sort it into a group based on its attributes. This helps you describe the shape clearly and accurately.
- A shape with four equal sides and four right angles is classified as a square.
- A shape with two pairs of parallel sides and four right angles is classified as a rectangle.
- A shape with one pair of parallel sides is classified as a trapezoid.
Always look at several attributes before naming a shape. Some shapes share traits, so one clue is not always enough.