NCERT Solutions for Class 7 Maths Chapter 14 – Symmetry

NCERT Solutions for Class 7 Maths Chapter 14 is about a powerful geometrical concept of Symmetry which we see everywhere around us in manmade and natural objects. In this chapter, there are a total of 3 exercises and 19 questions that are based on various topics of Symmetry. The NCERT Book Class 7 Chapter 14 covers the concept of line and rotational Symmetry. We also study lines of Symmetry of regular polygons in this chapter.  

NCERT Solutions for Class 7 Chapter 14 ‘Symmetry’ is based on the latest CBSE approved syllabus. We, at Instasolv, provide the most reliable study material for Class 7 Maths. Instasolv also provides chapter-wise solutions of NCERT Class 7 Maths Book that help you in understanding the concepts of each topic better.

You learn to use the concept of NCERT Class 7 Chapter 14 that we see all around us in nature. Humans have also taken inspiration from nature and most man-made objects also use the concept of Symmetry. You will be able to strengthen your concepts and score high in the exams through our NCERT Solutions. 

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry: Important Topics


  • Leaves, flowers, animals, are all examples of Symmetry that nature has provided us with. Furniture, jewelry, buildings are examples of manmade objects which also use the geometrical concept of Symmetry.
  • We have already been introduced to line Symmetry in earlier classes. A figure is said to have line Symmetry if there is a line about which if the figure is folded, the two parts of the figure will coincide. 

Lines of Symmetry for Regular Polygons 

  • A polygon is a closed figure. It is made up of line segments. The triangle is a type of polygon having the least number of line segments equal to three. A polygon is said to be regular if all its sides are of equal length and all its angles are of equal measure. An equilateral triangle is a regular polygon of three sides. 
  • Square is a regular polygon of four sides. A regular pentagon has five equal sides and all its angles measure seventy-two degrees. Similarly, a regular hexagon has six equal sides and its angles measure sixty degrees. 
  • Lines of Symmetry for a regular polygon are equal to the number of sides of the polygon. Each line of Symmetry can be drawn through the vertices of the regular polygon. 
  • An equilateral triangle will have three lines of Symmetry, a square four lines of Symmetry, a regular pentagon five lines of Symmetry, a regular hexagon six lines of Symmetry and so on. 

Rotational Symmetry 

  • A clock is used as the standard object to define rotation in scientific terms. Clockwise implies a rotation in the same direction as the movement of the hands of a clock. The rotation in the opposite direction is called anti-clockwise.
  • Like the hands of a clock, the movement is around a fixed point. The object is turned about the fixed point in the rotation. The fixed point is called the center of rotation.
  • The hand of a  clock depicting minutes rotates a full circle around the center of rotation in one hour. The angle of rotation in one hour for the minute’s hand of a clock is three hundred and sixty degrees. 
  • So in fifteen minutes, the hand would rotate at an angle of sixty degrees and in thirty minutes it would rotate by one hundred and eighty degrees. This angle of turning during rotation is called the angle of rotation. 

For Example A ceiling fan that has four arms of equal length. If you look up at the ceiling fan and take a picture. The same image will be seen if the fan is moved by every ninety degrees until the whole circle is completed. We see a rotational Symmetry of order four.

  • Similarly, fix the initial position of a square. The same image is seen on moving clockwise or anti-clockwise by an angle of ninety degrees. Each time we move clockwise or anti-clockwise by ninety degrees the same image can be seen until we complete three hundred and sixty degrees. Thus, the square also has rotational Symmetry of order four about its center. 

Line Symmetry and Rotational Symmetry 

  • For the square, we saw that it has line Symmetry as well as rotational Symmetry. The circle is the perfect symmetrical shape. Rotate it by any angle and the same image can be seen. 
  • For the circle, any line through its center or any diagonal forms a line of Symmetry. The circle has rotational Symmetry for any angle around its center. The circle can be said to have unlimited or infinite Symmetry.

To summarize, shapes could have only line Symmetry, only rotational Symmetry or both. 

Study Tips for NCERT Class 7 Maths  Chapter 14: Symmetry

Every student aims to get a high score in the exams. Instasolv recommends that you read chapter 14 Symmetry of CBSE NCERT Solutions for Class 7 Maths. Instasolv has provided a simple explanation and summary of each part. All of this can be used to develop a better understanding of all the concepts. 

  • If any concept is still not understood, ask the experts on the Instasolv app which does not charge any student for this support. 
  • This exercise requires good visualization. You can get answers to direct questions from the summary explained above. For other questions, here are some tips:
    1. Check for the shapes, whether they have line Symmetry or rotational Symmetry or both
    2. For line Symmetry, use the vertices as the start of a line and take a cross-section across the shape. Lines of Symmetry are likely to be through a vertex.
    3. For rotational Symmetry, check the center of rotation which is generally the central point of the shape. If there are arms to the object or shape, three hundred and sixty degrees divided by the number of arms is likely to be the angle of rotation. 
  •  There are several self-practice exercises and Instasolv recommends that you do all of them without looking at the solutions. 

Learning by rote is never recommended by the subject matter experts of Instasolv. In this chapter, understanding the concept and being able to visualize the patterns formed by reflection or rotation is important. Only this understanding and not answers learned by rote will help you answer all the questions easily in the exams.

Follow the NCERT Solutions and our expert’s tips provided and score high marks in your CBSE Maths exam.