CBSE Class 7 Mathematics Chapter 14: Symmetry NCERT Solutions
CBSE Class 7 Mathematics Chapter 14, Symmetry, introduces students to the fascinating world of symmetrical shapes. This chapter explores the concept of a line of symmetry, which divides a shape into two identical halves. Through engaging explanations and practical examples, students will learn to identify and draw lines of symmetry in various geometric figures, from simple shapes like squares and circles to more complex patterns. The NCERT Solutions for this chapter offer clear, step-by-step guidance to help students master these concepts. Understanding symmetry not only enhances geometrical understanding but also helps in recognizing patterns in the world around us, making learning both fun and educational.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 7 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 14 |
Chapter summary
Chapter 14, Symmetry, for Class 7 Mathematics NCERT Solutions focuses on understanding and identifying lines of symmetry in various figures. The exercises cover drawing axes of symmetry for different shapes, including regular polygons and irregular figures. This chapter helps students develop spatial reasoning skills by analyzing the reflective properties of shapes.
Learning outcomes
- Understand the concept of symmetry.
- Identify the line(s) of symmetry in given figures.
- Draw the axes of symmetry for various geometric shapes.
- Differentiate between figures with and without symmetry.
- Recognize symmetry in everyday objects.
Topics covered
Paper topics
- Symmetry
- Line of Symmetry
- Axes of Symmetry
- Geometric Shapes
- Reflection
- Regular Polygons
- Irregular Figures
- Identifying Symmetry
Important topics
- Definition of Line of Symmetry
- Finding Lines of Symmetry in Squares
- Finding Lines of Symmetry in Rectangles
- Finding Lines of Symmetry in Triangles
- Symmetry in Letters and Numbers
PDF preview
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Questions and Solutions
Question 1
The figures are represented by punched holes in various patterns.
To find the axes of symmetry for each figure, we need to identify the line(s) along which the figure can be folded so that the two halves match exactly. This line is called the line of symmetry or axis of symmetry.
Let's analyze each figure:
- (a) This figure has one vertical line of symmetry passing through the center.
Axis of symmetry: Vertical line through the center.
- (b) This figure, resembling a square, has four lines of symmetry: one horizontal, one vertical, and two diagonals.
Axes of symmetry: Horizontal, vertical, and two diagonal lines.
- (c) This figure has one vertical line of symmetry passing through the center.
Axis of symmetry: Vertical line through the center.
- (d) This figure has one horizontal line of symmetry passing through the center.
Axis of symmetry: Horizontal line through the center.
- (e) This figure has one vertical line of symmetry passing through the center.
Axis of symmetry: Vertical line through the center.
- (f) This figure has one horizontal line of symmetry passing through the center.
Axis of symmetry: Horizontal line through the center.
- (g) This figure has one vertical line of symmetry passing through the center.
Axis of symmetry: Vertical line through the center.
- (h) This figure has one horizontal line of symmetry passing through the center.
Axis of symmetry: Horizontal line through the center.
- (i) This figure has two lines of symmetry: one vertical and one horizontal, both passing through the center.
Axes of symmetry: Vertical and horizontal lines through the center.
- (j) This figure has one vertical line of symmetry passing through the center.
Axis of symmetry: Vertical line through the center.
- (k) This figure has one horizontal line of symmetry passing through the center.
Axis of symmetry: Horizontal line through the center.
- (l) This figure has one vertical line of symmetry passing through the center.
Axis of symmetry: Vertical line through the center.
Common mistakes
- Confusing rotational symmetry with line symmetry.
- Incorrectly identifying all possible lines of symmetry.
- Failing to recognize symmetry in irregular shapes.
- Overlooking symmetry in figures with multiple lines.
Revision tips
- Practice drawing lines of symmetry on various shapes.
- Use a mirror to visualize lines of symmetry for real-world objects.
- Review the definitions of symmetry and line of symmetry.
- Attempt to find symmetry in letters of the alphabet and numbers.
Practice MCQs
Q1. What is a line of symmetry?
Explanation: A line of symmetry is a line that divides a figure into two mirror-image halves, meaning one half is the reflection of the other across this line.
Q2. How many lines of symmetry does a square have?
Explanation: A square has four lines of symmetry: two diagonals and two lines joining the midpoints of opposite sides.
Q3. Which of the following letters of the English alphabet has only one vertical line of symmetry?
Explanation: The letter 'A' has a single vertical line of symmetry. Letters like B, C, and D have a horizontal line of symmetry.
Q4. An irregular pentagon typically has:
Explanation: An irregular pentagon, by definition, has sides and angles of different measures, and therefore, it does not possess any line of symmetry.
Q5. What is the line of symmetry for an isosceles triangle?
Explanation: In an isosceles triangle, the altitude to the base, the median to the base, and the angle bisector of the vertex angle all coincide and form the single line of symmetry.
Frequently asked questions
What is Chapter 14 of Class 7 Mathematics about?
Chapter 14 of Class 7 Mathematics NCERT Solutions covers the concept of Symmetry, focusing on identifying and drawing lines of symmetry in various geometric figures.
What is a line of symmetry?
A line of symmetry is a line that divides a figure into two identical halves that are mirror images of each other.
How can these NCERT Solutions help students?
These solutions provide clear, step-by-step explanations for each question in Chapter 14, helping students understand the concept of symmetry and how to apply it to different shapes for better learning and exam revision.
Does this chapter cover rotational symmetry?
This chapter primarily focuses on line symmetry (or reflectional symmetry). Rotational symmetry is a different concept.
Are there lines of symmetry in all shapes?
No, not all shapes have lines of symmetry. Some shapes are asymmetrical, meaning they cannot be divided into two identical mirror-image halves by any line.
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