Symmetry is a fascinating concept that we see all around us in nature, art, and everyday life. It is the property that makes an object look the same when viewed from different directions or after certain changes, like flipping or turning. In RD Sharma Class 7 Maths Chapter 18 – Symmetry, students learn about the different types of symmetry, how to identify them, and how to apply this knowledge in practical situations. This chapter helps build not only mathematical skills but also observational and creative thinking abilities. When we talk about symmetry in mathematics, we usually mean geometrical symmetry. A figure is said to be symmetrical if it can be divided into two identical halves that are mirror images of each other.
The line that divides the figure into these halves is called the line of symmetry or axis of symmetry. This idea is not just a part of geometry—it can be found in leaves, flowers, animals, buildings, and even in human faces. The chapter begins by explaining line symmetry in simple terms. Students will see how shapes like squares, rectangles, circles, and equilateral triangles have lines of symmetry. They will also learn to count the number of symmetry lines for a given figure. For example, a square has four lines of symmetry, while a circle has an infinite number. Next, the chapter introduces the idea of rotational symmetry—when a shape looks the same after being rotated by a certain angle around its center.
The order of rotational symmetry tells us how many times a figure matches itself during a full turn of 360 degrees. For instance, an equilateral triangle has rotational symmetry of order 3. Through the solutions provided in RD Sharma, students get step-by-step explanations and solved examples that make it easy to understand these concepts. The exercises include identifying symmetry in given figures, drawing symmetrical shapes, and finding lines of symmetry in real-life objects. These solutions are written in a clear, student-friendly manner, allowing learners to follow along without confusion. By the end of the chapter, students will not only be able to recognize symmetry in various shapes but also appreciate its beauty in the world around them.
Do Check: RD Sharma Solutions for Class 7
Learning symmetry improves visual thinking, problem-solving skills, and attention to detail—qualities that are useful in many areas beyond mathematics. In short, RD Sharma’s solutions for Class 7 Chapter 18 make symmetry an interesting and enjoyable topic, turning mathematical ideas into something students can see, touch, and experience in their daily lives.
Download RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry PDF Here
You can easily download the RD Sharma Solutions for Class 7 Maths Chapter 18 – Symmetry PDF from here and study anytime, anywhere. This PDF contains clear, step-by-step answers to all the questions in the textbook, making it easier for students to understand the concepts of symmetry. Having the PDF means you can revise quickly before exams, practice at your own pace, and refer to the solutions whenever you get stuck. It’s a handy resource for scoring better marks and building strong maths skills.
Class 7 Maths Chapter 18 Symmetry Solutions - Download Now
Access Answers to RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry
Q1. How many lines of symmetry do these shapes have?
Below is a quick look at common figures and their lines of symmetry. A “line of symmetry” splits a shape into two mirror parts.
| Shape | Number of Lines of Symmetry | Simple Reason |
| (i) Equilateral Triangle | 3 | Each line from a vertex to the midpoint of the opposite side creates two equal mirror halves. |
| (ii) Isosceles Triangle | 1 | The line from the top vertex to the middle of the base splits it into two equal parts. |
| (iii) Scalene Triangle | 0 | All sides and angles are different, so no mirror line exists. |
| (iv) Rectangle | 2 | One vertical and one horizontal line through the center make mirror halves. |
| (v) Rhombus | 2 | Both diagonals act as mirror lines. |
| (vi) Square | 4 | Two diagonals and two midlines (vertical and horizontal) are symmetry lines. |
| (vii) Parallelogram | 0 | Unless it is a rectangle or a rhombus with special properties, it has no mirror line. |
| (viii) General Quadrilateral | 0 | No special equal sides or angles, so no symmetry line. |
| (ix) Regular Pentagon | 5 | All sides and angles are equal, giving five mirror lines. |
| (x) Regular Hexagon | 6 | Equal sides and angles give six mirror lines. |
| (xi) Circle | Infinitely many | Every diameter is a line of symmetry. |
| (xii) Semi-circle | 1 | The line through the center, perpendicular to the diameter, is the only mirror line. |
Q2. Rotational symmetry: fill in the table
“Rotational symmetry” means the shape looks the same after a turn (less than a full 360°) around a fixed point (the center of rotation).
| Shape | Centre of Rotation | Order of Rotation | Smallest Angle of Rotation |
| Square | Intersection of diagonals | 4 | 90° |
| Rectangle | Intersection of diagonals | 2 | 180° |
| Rhombus | Intersection of diagonals | 2 | 180° |
| Equilateral Triangle | Centroid (common center) | 3 | 120° |
| Regular Hexagon | Center of the hexagon | 6 | 60° |
| Circle | Center | Infinite | Any angle |
| Semi-circle | — | None (only 360°) | — |
Q3. Symmetry in English capital letters
For block-style uppercase letters, the table shows line symmetry and rotational symmetry.
| Letter | Line Symmetry? | Number of Lines | Rotational Symmetry? | Order of Rotation |
| Z | No | 0 | Yes | 2 |
| S | No | 0 | Yes | 2 |
| H | Yes | 2 (vertical & horizontal) | Yes | 2 |
| O | Yes | 2 (vertical & horizontal) | Yes | 2 |
| E | Yes | 1 (horizontal) | No | 0 |
| N | No | 0 | Yes | 2 |
| C | Yes | 1 (horizontal) | No | 0 |
Q4. Name a shape with no line symmetry and no rotational symmetry.
A scalene triangle is a good example. It has no mirror line and does not match itself on any turn less than 360°.
Q5. Pick English letters with given symmetry
(i) No line symmetry: Z
(ii) Rotational symmetry of order 2: N
These choices follow the common block-letter style used in school geometry.
Q6. Does a semi-circle have line or rotational symmetry?
A semi-circle has one line of symmetry. This line passes through the center and is perpendicular to the diameter (it cuts the flat edge into two equal parts). A semi-circle does not have rotational symmetry for any turn less than 360°, because after a half-turn (180°) the curved part and the flat side swap places and do not match the original.