NCERT Solutions for Class 7 Maths Chapter 12 Symmetry

Class 7 Maths Chapter 12 Symmetry Chapter Overview

Symmetry is more than just a drawing exercise; it is a fundamental property of geometry that describes how shapes can be mapped onto themselves. In Class 7, the curriculum introduces students to two primary types of symmetry: Line Symmetry and Rotational Symmetry. Line symmetry involves folding a figure along a straight line so that the two halves match perfectly. Rotational symmetry, on the other hand, deals with spinning a figure around a fixed central point.

Understanding these concepts is essential for higher-level geometry and fields like architecture or engineering. This chapter teaches you how to identify the "Order of Rotational Symmetry" and the "Angle of Rotation." For instance, a square can be rotated four times within a full circle and still look identical to its original position. By the end of this chapter, you will be able to look at any regular polygon—like a pentagon or hexagon—and immediately determine its symmetrical properties using the class 7 maths chapter 12 symmetry question answer provided below.

Class 7 Maths Chapter 12 Symmetry Question Answer

Below are the detailed, step-by-step solutions for the key questions found in your NCERT textbook. These have been simplified to ensure they are easy to follow and help you score better in your assignments.

1. Identifying Lines of Symmetry in Punched Figures

Question: Copy the figures with punched holes and find the axes of symmetry for each.

Solution: To solve this, imagine folding the paper so that one hole falls exactly on top of the other.

• If two holes are placed vertically at the top and bottom corners, the line of symmetry is a horizontal line passing through the centre.

• If the holes are placed diagonally, the axis of symmetry will be the diagonal line connecting the other two corners.

• The key is to ensure that the "folded" part is a mirror image of the original.

2. Completing Figures with a Given Line of Symmetry

Question: Given the line of symmetry, find the other holes.

Solution: This is a classic exercise in Class 7 maths chapter 12 symmetry questions with answers. If a hole is punched on one side of the dotted line (the axis), you must mark a hole at the exact same distance on the opposite side.

• If the line is vertical, the hole moves horizontally across.

• If the line is horizontal, the hole moves vertically up or down.

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3. Lines of Symmetry in Regular Polygons

Question: State the number of lines of symmetry for an equilateral triangle, a square, and a regular pentagon.

Solution: For any regular polygon, the number of lines of symmetry is equal to the number of sides.

• Equilateral Triangle: 3 lines of symmetry (passing from each vertex to the midpoint of the opposite side).

• Square: 4 lines of symmetry (two connecting midpoints of opposite sides and two diagonals).

• Regular Pentagon: 5 lines of symmetry.

4. Understanding Rotational Symmetry

Question: Which of the following figures have rotational symmetry of order more than 1? (Circle, Square, Triangle).

Solution:

• Circle: Yes, it has an infinite order of rotational symmetry because it looks the same at every angle.

• Square: Yes, it has an order of 4.

• Equilateral Triangle: Yes, it has an order of 3.
  All these figures look identical to their original form more than once during a full 360-degree rotation.

5. Finding the Centre and Angle of Rotation

Question: Give the order of rotational symmetry and the angle of rotation for a square.

Solution:

• Centre of Rotation: The intersection point of the diagonals.

• Order of Rotational Symmetry: 4.

• Angle of Rotation: 360 / 4 = 90 degrees.
  This means every time you rotate a square by 90 degrees, it fits perfectly into its original boundary.

Read More - NCERT Solutions for Class 7 Maths Chapter 1 Integers

6. Symmetry in the Alphabet

Question: Which letters of the English alphabet have reflectional symmetry about a vertical mirror?

Solution: The letters that look the same when split vertically are: A, H, I, M, O, T, U, V, W, X, Y. This is a frequent topic in Class 7 chapter 12 symmetry NCERT solutions because it links maths to everyday objects.

7. Shapes with Both Line and Rotational Symmetry

Question: Name a quadrilateral which has both line and rotational symmetry of order more than 1.

Solution: A Square and a Rectangle are perfect examples.

• A square has 4 lines of symmetry and rotational order of 4.

• A rectangle has 2 lines of symmetry and rotational order of 2.

8. The Case of the Rhombus

Question: Describe the symmetry of a Rhombus.

Solution: A rhombus is unique. It has 2 lines of symmetry (its diagonals). Its order of rotational symmetry is 2, with an angle of rotation of 180 degrees. Unlike a square, its sides are equal but its angles are not all 90 degrees, which limits its symmetry.

9. Rotation Around a Vertex

Question: Can we have a rotational symmetry of order more than 1 whose angle of rotation is 45 degrees?

Solution: Yes. To check this, divide 360 by the given angle. If the result is a whole number, it is possible.

• 360 / 45 = 8.
  Since 8 is a whole number, a figure (like a regular octagon) can have an angle of rotation of 45 degrees.

10. Rotation with an Angle of 17 Degrees

Question: Can a figure have rotational symmetry with an angle of 17 degrees?

Solution: No. When we divide 360 by 17, the result is not a whole number (approximately 21.17). Therefore, a figure cannot have a rotational symmetry order based on a 17-degree angle.

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Class 7 Maths Chapter 12 Symmetry Question Answer Quick Preparation 

Studying symmetry requires a good sense of visualisation. Here are some simple tips to help you master the Class 7 Maths Chapter 12 Symmetry NCERT Solutions:

• Use a Pocket Mirror: If you are unsure where a line of symmetry lies, place a small mirror on your drawing. If the reflection matches the hidden half of the shape, you have correctly identified the axis.

• The 360 Rule: Always remember the formula: Angle of Rotation = 360 / Order of Symmetry. This simple division will help you verify your answers for any regular polygon.

• Trace and Rotate: If you cannot "see" the rotation in your head, trace the shape on a piece of transparent paper. Pin the centre with your pencil and rotate it. Count how many times it matches the original drawing underneath.

• Focus on Regular Polygons: Spend extra time learning the properties of equilateral triangles, squares, pentagons, and hexagons. Most exam questions for Class 7 chapter 12 symmetry question answer revolve around these shapes.

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