Line of Symmetry — Definition, Formula & Examples
A line of symmetry is a line that divides a shape into two halves that are exact mirror images of each other. If you folded the shape along this line, both sides would match up perfectly.
A line of symmetry is a line such that for every point on a figure, there exists a corresponding point on the figure where is the perpendicular bisector of segment . The figure is therefore invariant under reflection across .
How It Works
To find a line of symmetry, imagine folding the shape in half. If both sides line up exactly, the fold is a line of symmetry. Some shapes have no lines of symmetry, while others have many. A rectangle has 2 lines of symmetry (one vertical, one horizontal), and a circle has infinitely many because you can fold it through the center at any angle.
Example
Problem: How many lines of symmetry does an equilateral triangle have?
Step 1: Draw a line from each vertex (corner) to the midpoint of the opposite side.
Step 2: Check each line: fold the triangle along it. Since all three sides are equal, each fold produces two halves that match perfectly.
Step 3: Count the lines. There is one from each of the 3 vertices, giving 3 lines of symmetry.
Answer: An equilateral triangle has 3 lines of symmetry.
Why It Matters
Recognizing lines of symmetry helps you classify shapes in geometry and understand balance in art and design. In later math courses, lines of symmetry become axes of symmetry for parabolas and other graphs, which is essential for graphing functions in algebra.
Common Mistakes
Mistake: Thinking every line through the center of a shape is a line of symmetry.
Correction: A diagonal of a rectangle, for example, is not a line of symmetry because folding along it does not make the two halves match. Always check by imagining the fold.