Symmetry

Geometry · Axiom Academy

When shapes map perfectly onto themselves 1. Reflection: Folding a Figure in Half The most familiar symmetry is line symmetry (a reflection). A figure has it when you can fold along a line — the line of symmetry — and both halves land exactly on top of each other. Press play and watch the right half fold across the dashed line and map perfectly onto the left. A figure can have more than one line of symmetry. A square has four: two through the midpoints of opposite sides and two along the diagonals. Press play and watch the square fold across each axis in turn — every fold lands it back on itself, so the count climbs to four. Multiple lines of symmetry (a square has 4) Infinitely many (like a circle!) The number of lines of symmetry depends on the shape. Here are four familiar figures with their lines of symmetry drawn in. 3. Rotational Symmetry and Its Order Rotational symmetry turns a figure about a center by less than a full turn, and it looks unchanged. The order is the number of times a figure maps onto itself during one complete rotation (360°); the smallest turn that works is the angle of rotation. Press play and watch an equilateral triangle turn 120° onto itself. A figure has rotational symmetry if its order is 2 or greater. Order 3 — maps onto itself every 120°. Order 4 — maps onto itself every 90°. Order 5 — maps onto itself every 72°. Order 6 — maps onto itself every 60°. 4. Point Symmetry: The Half-Turn

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