Math exercise sheet for 5th graders focusing on rotational symmetry properties of geometric shapes.

Problem Analysis:

The task involves understanding rotational symmetry, its order, and the angle of rotational symmetry for various shapes. Let's break it down step by step.

#### Part 1: Fill up the given table
We need to determine the rotational symmetry, order of rotational symmetry, and angle of rotational symmetry for each shape provided in the table.

#### Definitions:
1. Rotational Symmetry: A shape has rotational symmetry if it looks the same after being rotated by a certain angle.
2. Order of Rotational Symmetry: The number of times a shape looks the same during a full rotation (360°).
3. Angle of Rotational Symmetry: The smallest angle by which the shape can be rotated to look the same.

#### Step-by-Step Solution for Each Shape:

1. Square (First Row):
- Rotational Symmetry: Yes
- Order of Rotational Symmetry: 4 (It looks the same at 0°, 90°, 180°, and 270°)
- Angle of Rotational Symmetry: 360° ÷ 4 = 90°

2. Rectangle (Second Row):
- Rotational Symmetry: Yes
- Order of Rotational Symmetry: 2 (It looks the same at 0° and 180°)
- Angle of Rotational Symmetry: 360° ÷ 2 = 180°

3. Equilateral Triangle (Third Row):
- Rotational Symmetry: Yes
- Order of Rotational Symmetry: 3 (It looks the same at 0°, 120°, and 240°)
- Angle of Rotational Symmetry: 360° ÷ 3 = 120°

4. Right-Angled Triangle (Fourth Row):
- Rotational Symmetry: No
- Order of Rotational Symmetry: 1 (It only looks the same at 0°)
- Angle of Rotational Symmetry: 360° ÷ 1 = 360°

5. Circle (Fifth Row):
- Rotational Symmetry: Yes
- Order of Rotational Symmetry: Infinite (It looks the same at any angle)
- Angle of Rotational Symmetry: Any angle (e.g., 360° ÷ ∞ ≈ 0°)

6. Ellipse (Sixth Row):
- Rotational Symmetry: Yes
- Order of Rotational Symmetry: 2 (It looks the same at 0° and 180°)
- Angle of Rotational Symmetry: 360° ÷ 2 = 180°

7. Rhombus (Seventh Row):
- Rotational Symmetry: Yes
- Order of Rotational Symmetry: 2 (It looks the same at 0° and 180°)
- Angle of Rotational Symmetry: 360° ÷ 2 = 180°

#### Filled Table:
| Shape | Rotational Symmetry | Order of Rotational Symmetry | Angle of Rotational Symmetry |
|---------------|---------------------|-------------------------------|------------------------------|
| Square | Yes | 4 | 90° |
| Rectangle | Yes | 2 | 180° |
| Equilateral Triangle | Yes | 3 | 120° |
| Right-Angled Triangle | No | 1 | 360° |
| Circle | Yes | Infinite | Any angle |
| Ellipse | Yes | 2 | 180° |
| Rhombus | Yes | 2 | 180° |

---

Part 2: Click on the correct option

#### Question a): Which alphabet has the order of rotation 2?
- H: Rotates to look the same at 0° and 180° → Order = 2
- E: Rotates to look the same at 0° and 180° → Order = 2
- C: Rotates to look the same at 0° and 180° → Order = 2
- A: Rotates to look the same at 0° and 180° → Order = 2

All options (H, E, C, A) have an order of rotation of 2. However, typically, such questions expect a single answer based on common examples. If we choose one, H is a standard example.

Answer: i) H

#### Question b): What is the angle of rotational symmetry of a rectangle in anti-clockwise direction?
- From Part 1, we determined that the order of rotational symmetry for a rectangle is 2.
- The angle of rotational symmetry is calculated as: \( \frac{360^\circ}{\text{Order}} = \frac{360^\circ}{2} = 180^\circ \).

Answer: 180°

---

Final Answers:

1. Filled Table:
| Shape | Rotational Symmetry | Order of Rotational Symmetry | Angle of Rotational Symmetry |
|---------------|---------------------|-------------------------------|------------------------------|
| Square | Yes | 4 | 90° |
| Rectangle | Yes | 2 | 180° |
| Equilateral Triangle | Yes | 3 | 120° |
| Right-Angled Triangle | No | 1 | 360° |
| Circle | Yes | Infinite | Any angle |
| Ellipse | Yes | 2 | 180° |
| Rhombus | Yes | 2 | 180° |

2. a) H
b) 180°

Boxed Final Answer:
\[
\boxed{\text{See filled table above; a) H, b) 180°}}
\]