The order of rotation of an isosceles triangle is 1. As stated in the reference, the "Order of symmetry of isosceles triangle will be 1 and the angle of rotational symmetry is 360 degrees."
Understanding Order of Rotation
The order of rotational symmetry refers to the number of times a shape can be rotated around its central point (or a specific point) within a full 360-degree turn and still look exactly the same as the original shape.
- Order 1: A shape with an order of rotation of 1 only looks the same after a full 360-degree rotation.
Why is the Order of Rotation 1 for an Isosceles Triangle?
An isosceles triangle is defined by having at least two sides of equal length and two equal angles. Unless it is also equilateral (where all sides and angles are equal), it only possesses one line of symmetry, which runs from the vertex between the two equal sides to the midpoint of the base.
Consider a typical non-equilateral isosceles triangle:
- Rotating it by any angle other than 360 degrees will result in a shape that does not perfectly overlap the original position.
- Only upon completing a full 360-degree rotation does the triangle return to its identical initial orientation.
This aligns with the information from the reference, confirming that its order of rotational symmetry is 1, with the angle of rotational symmetry being 360 degrees.
Summary Table
| Property | Isosceles Triangle (Non-Equilateral) |
|---|---|
| Order of Rotational Symmetry | 1 |
| Angle of Rotational Symmetry | 360 degrees |
| Lines of Symmetry | 1 |
This means a non-equilateral isosceles triangle has only trivial rotational symmetry – it only maps onto itself after a complete turn.
