Rotational Symmetry

Pre-Algebra · Axiom Academy

A figure has rotational symmetry when it lands on itself before a full turn — and counting those landings tells you everything. 1. A Figure That Lands on Itself A figure has rotational symmetry if you can turn it about its center by less than a full turn and it looks exactly the same as where it started. Watch the square below: a faint copy marks its starting position, and a corner is tagged so you can tell it really has rotated. At the turned square drops perfectly onto the original — a match . 2. The Order Is How Many Times It Matches The order of rotational symmetry is just a count: how many times the figure lands on itself as it rotates through one full turn (the return to start at is included). Below, an equilateral triangle turns once around while a counter ticks up every time it matches. Step 1: Start the figure in its original position. Step 2: Rotate it one full turn and count each time it lands on itself. Step 3: That total count is the order of rotational symmetry. 3. The Smallest Turn Is 360° ÷ Order If a figure lands on itself n times in a full turn, those landings are spread out evenly — so the smallest rotation that matches it is split into n equal parts. Below, a regular pentagon (order 5 ) sweeps out that smallest angle first, then steps through all five matches. smallest turn that matches the figure pentagon: order 5, so it matches every 72° 4. Yes or No: Does It Have Rotational Symmetry?

This is the written version of the interactive lesson above. See the full Pre-Algebra course.