# NCERT Solutions for Class 7 Mathematics Chapter 14 Symmetry

In order to help students with their Mathematics preparation, Extramarks offers NCERT Solutions for Class 7 Mathematics Chapter 14. These are comprehensive and precise solutions to problems covered in Chapter 14 of Class 7 NCERT Mathematics textbook. These solutions are prepared by subject matter experts that provide thorough step-by-step explanations to questions given in the chapter. Students can use these resources to prepare well for their final exams, for last-minute revisions, and for help with their assignments.

## NCERT Solutions for Class 7 Mathematics Chapter 14

### NCERT Solutions for Class 7 Mathematics Chapter 14

Chapter 14 of Class 7 Mathematics NCERT textbook introduces students to the concept of symmetry. We all have a general sense of what symmetry means. However, this chapter explains how mathematicians think about symmetry and how useful this concept is in almost all fields of study including physics, chemistry, biology, and more. In this chapter students will learn about the two major kinds of symmetry including line symmetry and rotational symmetry and how they apply to different kinds of geometrical shapes.

Students should go through the chapter and try to attempt all the problems covered in this chapter themselves. They can always use NCERT Solutions for Class 7 Mathematics Chapter 14 for reference if they are unable to comprehend or solve the problem.

### What is Symmetry?

Symmetry is an essential geometrical concept in Mathematics. The concept of symmetry is used in almost all actions of our everyday life. Symmetry is when an object can be divided into several parts that are all mirror images of themselves. Students will be introduced to major kinds of symmetries in this chapter including line symmetry and rotational symmetry.

### Facts

• Regular polygons have equal sides and equal angles. They have more than one or multiple lines of symmetry.
• A square has four lines of symmetry.
• A regular pentagon has five lines of symmetry.
• A regular hexagon has six lines of symmetry.
• The rotation of an object occurs around a fixed point called the centre of rotation.
• The angle by which an object rotates is called the angle of rotation.
• A half-turn means a rotation by 180 degrees.
• After a rotation, if an object looks the same, it is said to exhibit rotational symmetry.

### Line of Symmetry

In this chapter, students will learn the meaning of the line of symmetry for a specific figure. When a line divides a figure or a shape into two identical parts, it is said that the shape exhibits symmetry. The line that divides the shape is called the line of symmetry. A figure has a line of symmetry if there is a line about which the figure can be folded into two coinciding parts. The line of symmetry is also called the axis of symmetry.

The idea of symmetry is exhibited in nature in tree leaves, flowers, etc. Symmetrical designs are used by manufacturers, artists, architects, designers, etc.

### Line of Symmetry for Regular Polygons:

A polygon is a closed figure made of only line segments. Since a polygon has to be a closed figure, the minimum number of line segments required to create a polygon is three and the resulting polygon is nothing but a triangle. A polygon is called regular if all the sides are equal in length and all its angles are equal. An equilateral triangle is a regular polygon. A square is also a regular polygon.

An equilateral triangle has sides the same length, and each of its angles measures 600. An equilateral triangle has three lines of symmetry.

A square is also a regular polygon because all its sides are equal, and each of its angles is a right angle. A square has four lines of symmetry.

### Rotational Symmetry

The other kind of symmetry that students learn about in this chapter is rotational symmetry. Rotational symmetry occurs when the size and shape of an object do not change when it rotates about a fixed point. This fixed point where the rotation occurs is called the centre of rotation. The angle through which the body turns is called the rotation angle.

1. A complete turn means a rotation by 3600
2. A half-turn means a rotation by 1800
3. A quarter-turn means a rotation by 900

If a figure can be rotated less than 3600 around a point such that it coincides with itself, it has rotational symmetry.

Conclusion

Symmetry is an important chapter that carries a significant weightage in final exams. It is also a very useful topic to master as students will find the concepts learned here will be used in many other subjects as well. Students should solve as many problems as possible on the topic and can use NCERT Solutions for Class 7 Mathematics Chapter 14 for their reference.

### NCERT Solutions for Class 7 Mathematics

Class 7 Mathematics consists of a total of 15 chapters on various topics. Students can download detailed and accurate solutions to the questions covered in all these chapters from the Extramarks website. The different chapters covered in Class 7 Mathematics include:

• Chapter 1 - Integers
• Chapter 2 - Fractions and Decimals
• Chapter 3 - Data Handling
• Chapter 4 - Simple Equations
• Chapter 5 - Lines and Angles
• Chapter 6 - The Triangle and Its Properties
• Chapter 7 - Congruence of Triangles
• Chapter 8 - Comparing Quantities
• Chapter 9 - Rational Numbers
• Chapter 10 - Practical Geometry
• Chapter 11 - Perimeter and Area
• Chapter 12 - Algebraic Expressions
• Chapter 13 - Exponents and Powers
• Chapter 15 - Visualising Solid Shapes

### NCERT Solutions for Class 7

Along with mathematics, Extramarks provides solutions for all the subjects covered in Class 7. Apart from Class 7, students in other grades can also find detailed solutions to all of the problems covered in each chapter in each subject for their respective grades. Students can download online material for NCERT Solutions Class 1, NCERT Solutions Class 2, NCERT Solutions Class 3, NCERT Solutions Class 4, NCERT Solutions Class 5, NCERT Solutions Class 6, NCERT Solutions Class 7, NCERT Solutions Class 8, NCERT Solutions Class 9, NCERT Solutions Class 10, NCERT Solutions Class 11, and NCERT Solutions Class 12.

Q.1 Copy the figures with punched holes and find the axes of symmetry for the following:

Ans-

$\text{The axes of symmetry in the given figures are as follows:}$