Rotational symmetry
A figure has rotational symmetry if it looks exactly the same after being rotated less than 360 degrees around its center. A square has rotational symmetry at 90, 180, and 270 degrees; the letter S has rotational symmetry at 180 degrees. The number of times a figure looks identical during a full rotation is called its order of symmetry. In Grade 7 Saxon Math Course 2, Chapter 6, rotational symmetry is studied alongside reflective symmetry as part of geometric transformations, with real-world applications in art, architecture, and nature.
Key Concepts
Property A figure has rotational symmetry if it re appears in its original position more than once in a full turn.
Examples The letter 'S' has rotational symmetry because it looks the same after a half turn ($180^{\circ}$). A regular triangle has rotational symmetry because it looks identical after being rotated by $120^{\circ}$ and $240^{\circ}$. A square reappears in its original position after turns of $90^{\circ}$, $180^{\circ}$, and $270^{\circ}$.
Explanation Imagine spinning a shape around its center. If it looks exactly the same before you've completed a full $360^{\circ}$ rotation, it has rotational symmetry. It's like a fidget spinner that looks identical with each partial spin!
Common Questions
What is rotational symmetry?
A figure has rotational symmetry if it looks the same as the original after a rotation of less than 360 degrees about its center.
How do you find the angle of rotational symmetry?
Divide 360 degrees by the order of symmetry. A regular hexagon has order 6, so each rotation angle is 360 divided by 6 = 60 degrees.
What is the order of rotational symmetry?
The order is the number of times the figure matches the original in one full 360-degree rotation. A square has order 4 because it matches at 90, 180, 270, and 360 degrees.
Does every shape have rotational symmetry?
No. A scalene triangle, for example, only looks the same after a full 360-degree rotation, so it has order 1, which means no rotational symmetry.
When do 7th graders study rotational symmetry?
Saxon Math, Course 2, Chapter 6 covers rotational symmetry as part of the Grade 7 geometric transformations and symmetry unit.
How is rotational symmetry different from line symmetry?
Line symmetry (reflection symmetry) means a figure can be folded onto itself along a line. Rotational symmetry means a figure looks the same after a partial turn around a center point.