Polygons &
Properties.
A polygon is a plane, closed shape formed from the union of three or more line segments, joined end to end so that no two adjacent segments lie on the same straight line. This lesson explains every property of polygons in English, with diagrams, worked examples and interactive practice.
Learning Outcomes
- Learn the concept of a polygon.
- Distinguish between convex and concave polygons.
- Deduce the sum of the measures of the interior angles of a polygon.
- Learn what makes a polygon regular.
- Learn the concept of an axis of symmetry.
- Determine the axes of symmetry in polygons.
Vocabulary
What makes a shape a polygon?
- 1. Sides. The line segments forming the shape are called the polygon's sides.
- 2. Vertices. The segments intersect only at their endpoints; those points are the vertices.
- 3. No straight joins. No two adjacent segments lie on one straight line.
- 4. Naming. Every polygon is named after its number of sides.
- Number of sides = number of vertices = number of interior angles.
Angles, diagonals and notes
Interior angle
The angle included between two adjacent sides of the polygon.
Exterior angle
The angle between one side and the extension of the adjacent side.
Diagonal
Any segment joining two non-consecutive vertices. A quadrilateral has 2 diagonals; a pentagon has 5.
Lesson Map
Polygon Gallery
Triangle through decagon, side by side.
03Convex & Concave
Reflex angles and the straight-line test.
04Interior Angles
Deduce (n − 2) × 180° from triangles.
05Regular Polygons
Equal sides and equal angles.
06Axes of Symmetry
Fold lines and how many each shape has.
07Worked Examples
Step-by-step solutions and exercises.
08Practice Zone
Quizzes, matching and learning games.