Class 7 RS Aggarwal Chapter-18 Reflection and Rotational Symmetry Solutions - Solutions
FAQs on RS Aggarwal Class 7 Solutions Chapter-18 Reflection and Rotational Symmetry
1. What is the best way to use Vedantu’s RS Aggarwal Solutions for Class 7 Maths Chapter 18?
To effectively use the solutions for Chapter 18, first attempt to solve the exercises (18A and 18B) on your own. Then, refer to our solutions to verify your answers or understand the correct, step-by-step method for problems you found difficult. Our solutions are crafted by experts to clarify concepts like identifying the line of symmetry and determining the order of rotational symmetry, ensuring you build a strong conceptual foundation.
2. How do you find the line of symmetry for a complex geometric figure in the RS Aggarwal exercises?
To find the line of symmetry, imagine folding the figure along a line. If one half of the figure perfectly covers the other half, that line is a line of symmetry. For complex shapes, look for natural divisions. For example:
- In an isosceles trapezium, the line of symmetry is the one that joins the midpoints of the parallel sides.
- In a kite, the main diagonal is the line of symmetry.
- A regular pentagon has 5 lines of symmetry, each passing through a vertex and the midpoint of the opposite side.
3. What is the method to determine the order of rotational symmetry for any shape in Chapter 18?
The order of rotational symmetry is the number of times a figure fits onto itself during a full 360-degree rotation. To find it, follow these steps:
1. Identify the centre of rotation (the point the figure turns around).
2. Rotate the figure mentally or on paper.
3. Count how many times it looks exactly the same as its starting position before completing the full 360° turn.
For example, a square looks the same at 90°, 180°, 270°, and 360°, so its order of rotational symmetry is 4.
4. Can a figure have rotational symmetry but no line of symmetry? Please provide an example from the Class 7 syllabus.
Yes, a figure can have rotational symmetry without having any line of symmetry. A common example is a parallelogram. It does not have any line of symmetry because you cannot fold it onto itself perfectly. However, it has a rotational symmetry of order 2, as it looks the same after a 180-degree rotation about the intersection point of its diagonals.
5. What is a common mistake when identifying the centre of rotation in a figure?
A common mistake is assuming the centre of rotation is always the visual or geometric centre. While this is true for regular polygons like squares and equilateral triangles, it is not always the case. For instance, in figures like the English letter 'S' or 'Z', the centre of rotation is the midpoint of the central segment, a point that students might overlook. The true centre of rotation is the single fixed point around which all other points on the figure move in a circle.
6. How does reflectional symmetry differ from rotational symmetry when solving problems?
The key difference lies in the transformation type:
- Reflectional symmetry is about flipping a figure across a line (the mirror line). When solving problems, you are looking for a line that divides the figure into two identical mirror-image halves.
- Rotational symmetry is about turning a figure around a central point. In problems, you identify a point and an angle of rotation (less than 360°) that makes the figure look unchanged.
7. Why are the solutions for Exercise 18A and Exercise 18B structured differently in RS Aggarwal Class 7?
The solutions are structured differently because each exercise targets a distinct concept. Exercise 18A primarily focuses on reflectional symmetry, so the solutions demonstrate how to identify and draw lines of symmetry. In contrast, Exercise 18B deals with rotational symmetry, so its solutions focus on calculating the order of rotation, the angle of rotation, and locating the centre of rotation for various geometric shapes.
