Symmetry
Line and rotational symmetry of shapes.
Key idea
Line and rotational symmetry of shapes.
In depth
A shape has line symmetry if a mirror line maps it onto itself, and rotational symmetry if some turn less than 360° does. The order of rotational symmetry counts how many times it fits in a full turn.
Worked example
An equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.
Real-world uses
- Designing logos and snowflake patterns
- Checking whether a face or building is balanced
Common mistake
Counting the identity rotation twice or forgetting diagonal lines.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Symmetry?
Line and rotational symmetry of shapes. It is a topic at the intermediate level in Geometry.
Where is Symmetry used in real life?
Real-world examples: Designing logos and snowflake patterns; Checking whether a face or building is balanced.
What should I learn before Symmetry?
Make sure you are comfortable with Dilations, the previous topic in Geometry.
What is a common mistake with Symmetry?
Counting the identity rotation twice or forgetting diagonal lines.
How can I practise Symmetry?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Symmetry?
Move on to Tessellations next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.