A figure has line symmetry if it can be folded along a line so that the two halves match exactly. The fold line is called the line of symmetry (or axis of symmetry). Some figures have one line of symmetry (like the letter A), some have multiple (a square has four), and some have none (a scalene triangle). Recognizing symmetry develops spatial reasoning and is important in art, design, nature, and later mathematics (symmetry of graphs, geometric transformations).
Fold paper cutouts to test for symmetry physically. Use mirrors along a proposed line of symmetry to see if the reflection completes the shape. Have students draw lines of symmetry on letters, shapes, and real-world images. Challenge students to find all lines of symmetry for regular polygons.
A line of symmetry is a line that divides a figure into two halves that are mirror images of each other — the two halves match exactly when the shape is folded along that line. Think of folding a piece of paper: if you can fold the figure so that both halves align perfectly and no part sticks out, the fold line is a line of symmetry. You've worked with lines, rays, and segments, so you can think of the line of symmetry as a special line with a particular relationship to the shape: every point on one side has a matching point at the same distance on the other side.
Not every shape has a line of symmetry, and those that do may have exactly one or several. The letter A has one vertical line of symmetry. A square has four — the two midlines (horizontal and vertical) and the two diagonals. An equilateral triangle has three lines of symmetry, one through each vertex and the midpoint of the opposite side. A regular polygon with n sides always has exactly n lines of symmetry, which is one reason regular polygons feel visually balanced and pleasing. A scalene triangle (all different side lengths) has zero.
A common trap with rectangles: it seems like the diagonal should be a line of symmetry because it "divides the rectangle in half," but half in area is not the same as half in shape. If you fold a non-square rectangle along a diagonal, the corners don't match — you get a right triangle overlapping a right triangle, but the long sides overhang. Only the horizontal and vertical midlines fold a rectangle so both halves line up perfectly. For a square, the diagonals also work, because all sides are equal.
Line symmetry shows up everywhere once you start looking: butterfly wings, human faces (approximately), letters of the alphabet, snowflakes, architectural facades, and leaf shapes. In mathematics, it reappears in function graphs — a parabola is symmetric about its vertical axis of symmetry, a foundational concept in algebra. The geometric intuition you build now — what it means for two halves to "match" — carries forward directly into those more abstract settings.