Visual guide to the lines of symmetry and rotational symmetry orders for common geometric shapes like squares, rectangles, and hexagons.

Problem Analysis:

The task involves identifying the rotational symmetry of various geometric shapes. Rotational symmetry is defined as the property of a shape that allows it to look identical after being rotated by a certain angle around its center. The order of rotational symmetry is the number of times the shape looks the same during a full rotation (360°).

Solution Explanation:

#### 1. Square
- Shape: A square has all sides equal and all angles equal to 90°.
- Rotational Symmetry:
- When rotated by 90°, the square looks the same.
- It will look the same at 180°, 270°, and 360° rotations.
- Total: 4 positions where the square looks identical.
- Order of Rotational Symmetry: 4

#### 2. Rectangle
- Shape: A rectangle has opposite sides equal and all angles equal to 90°.
- Rotational Symmetry:
- When rotated by 180°, the rectangle looks the same.
- It will also look the same at 360° rotation.
- Total: 2 positions where the rectangle looks identical.
- Order of Rotational Symmetry: 2

#### 3. Rhombus
- Shape: A rhombus has all sides equal but angles may differ.
- Rotational Symmetry:
- When rotated by 180°, the rhombus looks the same.
- It will also look the same at 360° rotation.
- Total: 2 positions where the rhombus looks identical.
- Order of Rotational Symmetry: 2

#### 4. Kite
- Shape: A kite has two pairs of adjacent sides equal.
- Rotational Symmetry:
- The kite does not look the same after any rotation other than 360°.
- Total: 1 position where the kite looks identical.
- Order of Rotational Symmetry: 1

#### 5. Parallelogram
- Shape: A parallelogram has opposite sides equal and parallel.
- Rotational Symmetry:
- When rotated by 180°, the parallelogram looks the same.
- It will also look the same at 360° rotation.
- Total: 2 positions where the parallelogram looks identical.
- Order of Rotational Symmetry: 2

#### 6. Equilateral Triangle
- Shape: An equilateral triangle has all sides equal and all angles equal to 60°.
- Rotational Symmetry:
- When rotated by 120°, the triangle looks the same.
- It will also look the same at 240° and 360° rotations.
- Total: 3 positions where the triangle looks identical.
- Order of Rotational Symmetry: 3

#### 7. Isosceles Trapezium
- Shape: An isosceles trapezium has one pair of parallel sides and the non-parallel sides are equal.
- Rotational Symmetry:
- The isosceles trapezium does not look the same after any rotation other than 360°.
- Total: 1 position where the trapezium looks identical.
- Order of Rotational Symmetry: 1

#### 8. Hexagon
- Shape: A regular hexagon has all sides equal and all angles equal.
- Rotational Symmetry:
- When rotated by 60°, the hexagon looks the same.
- It will also look the same at 120°, 180°, 240°, 300°, and 360° rotations.
- Total: 6 positions where the hexagon looks identical.
- Order of Rotational Symmetry: 6

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Square} & \text{Order 4} \\
\text{Rectangle} & \text{Order 2} \\
\text{Rhombus} & \text{Order 2} \\
\text{Kite} & \text{Order 1} \\
\text{Parallelogram} & \text{Order 2} \\
\text{Equilateral Triangle} & \text{Order 3} \\
\text{Isosceles Trapezium} & \text{Order 1} \\
\text{Hexagon} & \text{Order 6} \\
\end{array}
}
\]