Quadrilaterals
Properties of squares, rectangles, rhombi, trapezoids and kites.
Key idea
Properties of squares, rectangles, rhombi, trapezoids and kites.
In depth
Quadrilaterals have four sides and angles summing to 360°. Special ones form a family: square ⊂ rectangle ⊂ parallelogram ⊂ trapezium (inclusive definition), and square ⊂ rhombus ⊂ parallelogram. Each has its own properties for sides, angles, diagonals.
Worked example
A rectangle has equal diagonals; a rhombus has perpendicular diagonals; a square has both.
Real-world uses
- Identifying shapes in architecture, furniture and screen layouts
- Classifying parts of a flag
Common mistake
Treating categories as separate when a square is also a rectangle and a rhombus.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Quadrilaterals?
Properties of squares, rectangles, rhombi, trapezoids and kites. It is a topic at the intermediate level in Geometry.
Where is Quadrilaterals used in real life?
Real-world examples: Identifying shapes in architecture, furniture and screen layouts; Classifying parts of a flag.
What should I learn before Quadrilaterals?
Make sure you are comfortable with Area of Rhombus and Kite, the previous topic in Geometry.
What is a common mistake with Quadrilaterals?
Treating categories as separate when a square is also a rectangle and a rhombus.
How can I practise Quadrilaterals?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Quadrilaterals?
Move on to Polygons next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.