Quadrilaterals.

Unit 3 · Geometry and Measurement · Lesson Five

Quadrilaterals

Everything in this lesson grows from one fact: the four interior angles of any quadrilateral add up to 360°. From there we build trapeziums, parallelograms, and the conditions that let you prove a shape really is a parallelogram.

Learning outcomes

  • Understand the concept of a quadrilateral.
  • Deduce the sum of the interior angles of a quadrilateral.
  • Recognise and use the trapezium.
  • Recognise and use the parallelogram.
  • Determine when a quadrilateral becomes a parallelogram.
A quadrilateral is a closed plane figure made of four straight sides and four vertices.

Vocabulary

QuadrilateralTrapeziumParallelogramDiagonalInterior angle

The three key pictures

ABCD162345
Diagonal AC splits quadrilateral ABCD into two triangles: 180° + 180° = 360°.
ABCD
Trapezium ABCD: AB ∥ DC, while DA and CB are not parallel.
ABCD
Parallelogram ABCD: AB ∥ DC and AD ∥ BC.

Lesson map

01

The Sum of Interior Angles

Why every quadrilateral's four angles add up to exactly 360°, with the diagonal proof and worked examples.

02

The Trapezium

A quadrilateral with only two parallel sides — plus the isosceles and right trapezium special cases.

03

The Parallelogram

Definition and the four core properties: sides, diagonals, opposite angles and consecutive angles.

04

When Is It a Parallelogram?

The five conditions you can use to prove a quadrilateral is a parallelogram, with proof templates.

05

Activities & Games

Angle-sum solver, shape sorting, multiple-choice quiz, proof builder and a timed challenge.