Geometry · Lesson 10 of 18

Quadrilaterals and Their Properties

A quadrilateral has four straight sides and four angles that add to 360 degrees. Each type has its own sides and angles.

Primary
Updated 14 November 2026

What you will learn

Name the common quadrilaterals.
Describe their sides, angles and parallel lines.
Find a missing angle using the angle sum of $360^\circ$ .

Before you start: you should know parallel and perpendicular lines and the angles of a triangle. See Lines, Segments, Parallel and Perpendicular and Triangles.

The idea

A quadrilateral is a flat shape with four straight sides. Matching ticks on the sides show they are equal. Matching arrows show sides are parallel.

A square (4 equal sides, 4 right angles), a rectangle (opposite sides equal, 4 right angles) and a parallelogram (opposite sides equal and parallel).

A rhombus (4 equal sides), a trapezium (one pair of parallel sides) and a kite (two pairs of equal sides next to each other).

Angle sum

Cut any quadrilateral along a diagonal and you get two triangles. Each has angles adding to $180^\circ$ , so the four angles of a quadrilateral add to $2 \times 180^\circ = 360^\circ$ .

Properties at a glance

Parallel pairs and right angles for each shape. A square or rectangle may be called a special parallelogram.

Shapes can belong to more than one group. A square is a rectangle, a rhombus and a parallelogram all at once.

Worked examples

Example 1: Missing angle

Three angles in a quadrilateral are $85^\circ$ , $95^\circ$ and $110^\circ$ . Find the fourth.

$85 + 95 + 110 = 290$ .
$360 - 290 = 70$ .

Answer: $70^\circ$

Example 2: Which shape?

A shape has four equal sides but no right angles. What is it?

Four equal sides means a rhombus or a square.
No right angles rules out a square.

Answer: a rhombus

Example 3: Parallelogram angles

A parallelogram has one angle of $65^\circ$ . Find the other three.

Opposite angles are equal, so one more is $65^\circ$ .
Neighbouring angles add to $180^\circ$ : $180 - 65 = 115^\circ$ , and the last is also $115^\circ$ .
Check: $65 + 115 + 65 + 115 = 360$ .

Answer: $65^\circ$ , $115^\circ$ , $65^\circ$ , $115^\circ$

Tip: ask “is it a special case?” A square meets all the rules of a rectangle, so every square is a rectangle but not every rectangle is a square.

Why it matters

Quadrilaterals are in tiles, windows, screens, kites and bridges. Knowing their properties helps with area, symmetry and building accurately.