Line Symmetry
Line symmetry is the geometric property where one half of a figure is the mirror image of the other. Every regular polygon has as many lines of symmetry as it has sides: a square has 4, a regular hexagon has 6, an equilateral triangle has 3. This pattern is a beautiful mathematical discovery accessible through investigation. First Peoples art forms — birchbark biting, regalia borders, canoe designs — use bilateral symmetry as a fundamental design principle.
Lines of symmetry in regular polygons
Equilateral triangle: 3 lines of symmetry (each connects a vertex to the midpoint of the opposite side). Square: 4 lines (2 through opposite vertices, 2 through midpoints of opposite sides). Regular hexagon: 6 lines. Pattern: a regular n-gon has n lines of symmetry. This is a pattern discovery that connects geometry to number patterns.
Creating symmetrical designs
To create a symmetrical design, draw one half and reflect it across the line of symmetry. Every point on one side has a corresponding point exactly the same distance on the other side of the line. Folding along the line of symmetry should give two identical halves. This is the definition that students test with paper folding.
Symmetry in First Peoples art
Birchbark biting is a Nehiyaw and other First Peoples art form: folded birchbark is bitten through to create symmetrical patterns when unfolded. The symmetry is structurally guaranteed by the folding. Northwest Coast formline art uses bilateral symmetry to represent animals. Canoe building requires perfect bilateral symmetry for the canoe to track straight in water. These connections show that symmetry is a functional and aesthetic principle in cultural practice.