What Are Quadrilaterals?
Before we dive into specific shapes, let's make sure we're clear on the basics.
A closed two-dimensional shape with exactly four straight sides and four vertices (corners). The interior angles of every quadrilateral add up to 360°.
You already know some quadrilaterals — squares and rectangles are the most familiar ones. In this subtopic we'll explore three more members of the quadrilateral family that have their own special properties:
- Trapezium (also called a trapezoid in some countries)
- Rhombus
- Kite
Each of these shapes has a unique combination of side lengths, angle relationships, and diagonal properties that make it different from the others. These shapes appear all around us — in architecture, design, engineering, and even in nature — so understanding their properties is genuinely useful!
A great way to study quadrilaterals is to always ask four questions about any shape: (1) Which sides are equal? (2) Which sides are parallel? (3) What do the angles do? (4) What do the diagonals do?
The Trapezium
A quadrilateral with exactly one pair of parallel sides. The parallel sides are called the bases, and the non-parallel sides are called the legs.
Key properties of a trapezium:
- One pair of parallel sides (this is the defining property)
- The other pair of sides is not parallel
- On each side of the trapezium, the leg acts like a transversal cutting across the two parallel bases. This means the two interior angles on the same side of the leg add up to 180° — these pairs are sometimes called co-interior angles (or same-side interior angles)
- The sum of all four interior angles is 360° (as with every quadrilateral)
Think of a trapezium like the side view of a bucket or a lampshade — wider at one end, narrower at the other, with a flat top and bottom that never meet (because they're parallel).
Isosceles trapezium — a special trapezium where the two non-parallel sides (legs) are equal in length. In an isosceles trapezium:
- The base angles are equal (the two angles touching the longer base are equal, and the two angles touching the shorter base are equal)
- The diagonals are equal in length
11 more sections in this topic
Pick this up in your Library: it holds the whole topic, notes, cheatsheet and questions.