Lines of Symmetry | Rotational Symmetry | Maths Made Easy - Free Printable

Problem Analysis:

The image shows various geometric shapes along with their rotational symmetry orders. The task is to understand and explain the concept of rotational symmetry and how it applies to each shape.

#### Key Concepts:
1. Rotational Symmetry: A shape has rotational symmetry if it looks the same after being rotated by a certain angle around its center.
2. Order of Rotational Symmetry: The order of rotational symmetry is the number of times the shape looks identical during a full rotation (360°).

#### Steps to Solve:
1. Understand Each Shape's Symmetry:
- Analyze how many times each shape appears identical when rotated by 360°.
- Identify the angles at which the shape looks the same.

2. Verify the Given Orders:
- Compare the provided orders of rotational symmetry with the analysis.

3. Explain the Solution:
- Provide a detailed explanation for each shape.

---

Solution Explanation:

#### 1. Square
- Shape: A square has all sides equal and all angles equal (90°).
- Rotational Symmetry:
- When rotated by 90°, the square looks the same.
- It repeats this appearance at 180°, 270°, and 360°.
- Total rotations where it looks the same: 4.
- Order: 4
- Verification: Matches the given order.

#### 2. Rectangle
- Shape: A rectangle has opposite sides equal and all angles equal (90°).
- Rotational Symmetry:
- When rotated by 180°, the rectangle looks the same.
- It also looks the same at 360°.
- Total rotations where it looks the same: 2.
- Order: 2
- Verification: Matches the given order.

#### 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 also looks the same at 360°.
- Total rotations where it looks the same: 2.
- Order: 2
- Verification: Matches the given order.

#### 4. Kite
- Shape: A kite has two pairs of adjacent sides equal.
- Rotational Symmetry:
- The kite only looks the same after a full rotation of 360°.
- No other intermediate rotations make it look identical.
- Total rotations where it looks the same: 1.
- Order: 1
- Verification: Matches the given order.

#### 5. Parallelogram
- Shape: A parallelogram has opposite sides equal and parallel.
- Rotational Symmetry:
- When rotated by 180°, the parallelogram looks the same.
- It also looks the same at 360°.
- Total rotations where it looks the same: 2.
- Order: 2
- Verification: Matches the given order.

#### 6. Equilateral Triangle
- Shape: An equilateral triangle has all sides and angles equal.
- Rotational Symmetry:
- When rotated by 120°, the triangle looks the same.
- It repeats this appearance at 240° and 360°.
- Total rotations where it looks the same: 3.
- Order: 3
- Verification: Matches the given order.

#### 7. Isosceles Trapezium
- Shape: An isosceles trapezium has one pair of parallel sides and equal non-parallel sides.
- Rotational Symmetry:
- The isosceles trapezium only looks the same after a full rotation of 360°.
- No other intermediate rotations make it look identical.
- Total rotations where it looks the same: 1.
- Order: 1
- Verification: Matches the given order.

#### 8. Hexagon
- Shape: A regular hexagon has all sides and angles equal.
- Rotational Symmetry:
- When rotated by 60°, the hexagon looks the same.
- It repeats this appearance at 120°, 180°, 240°, 300°, and 360°.
- Total rotations where it looks the same: 6.
- Order: 6
- Verification: Matches the given order.

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Final Answer:

The provided orders of rotational symmetry for each shape are correct based on the analysis. The solution is verified as follows:

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