Quadrilaterals
Four-sided shapes are classified by sides and angles.
About this topic
A quadrilateral is a four-sided polygon whose interior angles total 360°. Special types include the parallelogram, rectangle, rhombus, square, trapezoid and kite, each with its own properties. They form a family tree, so a square is also a rectangle and a rhombus.
Classifying by sides, angles and diagonals helps you apply correct formulas. Quadrilaterals appear in architecture, tiling and structures, where rigidity depends on shape.
Worked example: a quadrilateral has angles 80°, 100°, 90° and x. Since the total is 360°, x = 90°. A shape with four equal sides could be a rhombus or a square, so check the angles or diagonals. A quadrilateral with exactly one pair of parallel sides is a trapezoid, while a kite has two pairs of adjacent equal sides and perpendicular diagonals.
Bridges and frames use triangles for rigidity because a four-sided frame can collapse into a different shape, which is why braces are added. Students often treat the names as separate boxes, but a square really belongs to several families. A frequent error is deciding by appearance in a diagram. Use properties instead: parallel sides, equal sides, right angles, and diagonals that bisect or are perpendicular. Work from the most specific name down.
Key ideas
- Angles sum to 360°
- Parallelogram, rectangle, rhombus, square, trapezoid, kite
- Properties pile up as shapes get more special
Quick check
Use cases: where Quadrilaterals helps
- Homework: review the key idea behind Quadrilaterals before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Quadrilaterals without notes.
- Visual learning: play with the interactive lab to see how Quadrilaterals changes when you adjust its inputs.
- Teaching a friend: explain Quadrilaterals in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Quadrilaterals?
Four-sided shapes are classified by sides and angles.
What will I learn in Quadrilaterals?
Angles sum to 360°. Parallelogram, rectangle, rhombus, square, trapezoid, kite. Properties pile up as shapes get more special.
Is Quadrilaterals part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Quadrilaterals lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Quadrilaterals?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.