An example of an object with no rotational symmetry is an arrow.
Rotational symmetry describes how a shape or object looks the same after being rotated by a certain amount around its center point, without completing a full 360-degree turn. If a shape only looks the same after a full 360-degree rotation, it is said to have no rotational symmetry, or rotational symmetry of order 1.
Based on the reference provided, an arrow and a right-angled triangle with different side lengths are examples of shapes that do not possess any rotational symmetry.
Why These Shapes Lack Rotational Symmetry
- The Arrow: An arrow is typically asymmetrical. If you rotate an arrow by any angle less than 360 degrees around its center, its orientation (the direction it points) changes, and it will not look the same as the original shape. Only after a full rotation does it return to its original appearance.
- A Right-Angled Triangle with Different Side Lengths: A triangle with a right angle and sides of unequal lengths (a scalene right triangle) also lacks rotational symmetry. Rotating such a triangle by any angle less than 360 degrees around its center will result in an orientation that is distinct from its starting position. For it to perfectly overlap its original position, a full 360-degree turn is required.
Understanding Rotational Symmetry Order
Shapes with rotational symmetry have an "order" of symmetry, which is the number of times the shape looks identical during a full 360-degree rotation.
- Order 1: No rotational symmetry (only looks the same at 360 degrees). Examples: arrow, scalene triangle.
- Order 2: Looks the same after a 180-degree rotation. Examples: rectangle, parallelogram.
- Order 3: Looks the same after 120-degree rotations. Example: equilateral triangle.
- Order 4: Looks the same after 90-degree rotations. Example: square.
Shapes like the arrow and the specific right-angled triangle described only match their original appearance after a 360-degree rotation, placing them in the category of having rotational symmetry of order 1, or simply, no rotational symmetry.
