Quadrilaterals

In short: A quadrilateral is a shape with 4 sides, and its angles add to $360^{\circ }$. Squares, rectangles, parallelograms, rhombuses, trapeziums and kites are special quadrilaterals, told apart by their equal sides, parallel sides and right angles.

Before you start

• Parallel lines go the same way and never meet, like train tracks. Diagrams mark them with matching arrows.
• The angles in a triangle add to $180^{\circ }$ (see Triangles).
• Angles on a straight line add to $180^{\circ }$.

Angle sum of a quadrilateral

The quadrilateral family

Using the parallel sides

In a parallelogram, two angles next to each other along a side add to $180^{\circ }$. (They are co-interior angles between parallel lines, explained in the next chapter.)

Exterior angles

If one side is stretched past a corner, the outside angle and the inside angle make a straight line. A quadrilateral with angles $130^{\circ }$, $95^{\circ }$ and $80^{\circ }$ has a fourth angle of $55^{\circ }$, and the exterior angle there is $180-55=125^{\circ }$.

Quick summary

• A quadrilateral has 4 sides and its angles add to $360^{\circ }$.
• Square: 4 equal sides, 4 right angles. Rectangle: opposite sides equal, 4 right angles.
• Parallelogram: opposite sides parallel and equal, opposite angles equal.
• Rhombus: 4 equal sides, opposite angles equal.
• Trapezium: exactly 1 pair of parallel sides.
• Kite: 2 pairs of equal sides next to each other, 1 pair of equal opposite angles.
• Neighbouring angles along a parallel side add to $180^{\circ }$.

Quiz