Reflection Symmetry — Definition, Formula & Examples
Reflection symmetry is when a shape can be divided by a line so that one half is a mirror image of the other half. The dividing line is called the line of symmetry.
A figure possesses reflection symmetry (also called line symmetry or bilateral symmetry) if there exists a line such that reflection across maps the figure onto itself. Every point on one side of has a corresponding point on the opposite side at an equal perpendicular distance from .
How It Works
To check for reflection symmetry, imagine folding the shape along a line. If the two halves overlap perfectly, that fold line is a line of symmetry. Some shapes have more than one line of symmetry — a square has four, and a circle has infinitely many. Other shapes, like a scalene triangle, have none at all. You can also test by measuring: each point on one side should be the same distance from the line as its matching point on the other side.
Worked Example
Problem: How many lines of symmetry does a regular hexagon have?
Step 1: A regular hexagon has 6 equal sides and 6 equal angles. A line of symmetry can run from any vertex to the opposite vertex.
Step 2: There are 3 such vertex-to-vertex lines. Additionally, a line of symmetry can run from the midpoint of one side to the midpoint of the opposite side, giving 3 more lines.
Step 3: Count the total lines of symmetry.
Answer: A regular hexagon has 6 lines of symmetry.
Why It Matters
Recognizing reflection symmetry helps you solve geometry problems faster — for instance, knowing a shape is symmetric lets you find missing side lengths or angles without extra measurements. Architects, designers, and artists use symmetry constantly to create balanced, visually appealing structures and patterns.
Common Mistakes
Mistake: Assuming every shape that 'looks balanced' has reflection symmetry.
Correction: A parallelogram looks balanced but has no lines of symmetry. Always verify by checking that folding along the proposed line makes both halves match exactly.