CBSE Class 7 Mathematics Chapter 14: Symmetry NCERT Solutions
This chapter on Symmetry for CBSE Class 7 Mathematics introduces students to the fundamental concepts of symmetry. The NCERT Solutions for Chapter 14 cover the identification of lines of symmetry in various geometric shapes and figures. Students will learn to determine whether a figure is symmetrical and how to draw the lines that divide it into two identical halves. The solutions provide clear explanations and step-by-step guidance for identifying axes of symmetry in given figures, including those with punched holes. This chapter is crucial for developing spatial reasoning and understanding geometric properties, which are essential for higher mathematics. These solutions will aid students in understanding the concepts thoroughly and preparing effectively for their exams by reinforcing their knowledge of symmetry.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 7 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 14: Symmetry |
Chapter summary
Chapter 14, Symmetry, for Class 7 Mathematics NCERT Solutions focuses on understanding and identifying lines of symmetry in various geometric figures. The exercises guide students through recognizing symmetrical shapes and drawing their axes of symmetry. This chapter builds foundational knowledge in geometry by exploring the concept of reflectional symmetry, which is key to understanding more complex geometric transformations.
Learning outcomes
- Understand the concept of symmetry.
- Identify the line(s) of symmetry in given figures.
- Draw the axes of symmetry for various shapes.
- Differentiate between symmetrical and asymmetrical figures.
- Apply the concept of symmetry to geometric shapes.
Topics covered
Paper topics
- Symmetry
- Lines of Symmetry
- Axes of Symmetry
- Geometric Figures
- Reflectional Symmetry
- Identifying Symmetry
- Drawing Axes of Symmetry
Important topics
- Lines of Symmetry
- Identifying Axes of Symmetry
- Symmetry in Geometric Shapes
- Reflectional Symmetry
PDF preview
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Questions and Solutions
Question 1
(a) A triangle with punched holes.
(b) A square with punched holes.
(c) A circle with punched holes.
(d) A pentagon with punched holes.
(e) A hexagon with punched holes.
(f) A rectangle with punched holes.
(g) A parallelogram with punched holes.
(h) A rhombus with punched holes.
(i) A kite with punched holes.
(j) A regular hexagon with punched holes.
(k) An irregular pentagon with punched holes.
(l) A regular octagon with punched holes.
To find the axes of symmetry for each figure, we need to identify lines along which the figure can be folded so that the two halves match exactly. This involves observing the shape and the placement of the punched holes.
- (a) Triangle: Depending on the type of triangle (equilateral, isosceles, or scalene) and the placement of holes, there could be 0, 1, or 3 axes of symmetry. For a general triangle with specific hole placements, we must check each potential line.
- (b) Square: A square has 4 axes of symmetry. These are the two diagonals and the lines joining the midpoints of opposite sides. The punched holes must be placed symmetrically with respect to these lines for them to be axes of symmetry.
- (c) Circle: A circle has infinitely many axes of symmetry, all passing through its center. The punched holes must be arranged in a way that maintains this symmetry.
- (d) Pentagon: A regular pentagon has 5 axes of symmetry, each passing through a vertex and the midpoint of the opposite side. For an irregular pentagon, the number of axes depends on its specific shape and hole placement.
- (e) Hexagon: A regular hexagon has 6 axes of symmetry. Three of these pass through opposite vertices, and the other three pass through the midpoints of opposite sides.
- (f) Rectangle: A rectangle has 2 axes of symmetry. These are the lines joining the midpoints of opposite sides. The diagonals are not axes of symmetry unless it is a square.
- (g) Parallelogram: A general parallelogram has no axes of symmetry. However, if the parallelogram is a rhombus or a rectangle, it will have axes of symmetry.
- (h) Rhombus: A rhombus has 2 axes of symmetry, which are its diagonals.
- (i) Kite: A kite has 1 axis of symmetry, which is the diagonal connecting the vertices where the equal sides meet.
- (j) Regular Hexagon: As mentioned in (e), a regular hexagon has 6 axes of symmetry.
- (k) Irregular Pentagon: An irregular pentagon generally has no axes of symmetry unless its specific shape and hole placement create one or more lines of symmetry.
- (l) Regular Octagon: A regular octagon has 8 axes of symmetry. Four of these pass through opposite vertices, and the other four pass through the midpoints of opposite sides.
The exact number and location of axes of symmetry depend on the specific configuration of the punched holes in each figure. Students are expected to draw these lines on their copied figures.
Common mistakes
- Incorrectly identifying the line of symmetry.
- Missing some or all axes of symmetry in a figure.
- Confusing symmetry with other geometric properties.
- Assuming all figures have at least one line of symmetry.
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 axes of symmetry.
- Attempt to find symmetry in everyday objects around you.
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.
Q2. How many lines of symmetry does a square have?
Explanation: A square has four lines of symmetry: two diagonals and two lines connecting the midpoints of opposite sides.
Q3. Which of the following figures typically has no line of symmetry?
Explanation: A scalene triangle has no sides or angles equal, and therefore, it does not have any line of symmetry.
Q4. What does it mean for a figure to be symmetrical?
Explanation: A figure is symmetrical if it can be folded along a line such that the two halves match exactly.
Q5. In Exercise 14.1, Question 1, what is the primary task for the students?
Explanation: The question asks students to copy the given figures with punched holes and then determine the axes of symmetry for each.
Frequently asked questions
What is the main focus of CBSE Class 7 Maths Chapter 14?
Chapter 14, Symmetry, focuses on understanding and identifying the lines of symmetry in various geometric shapes and figures.
How do these NCERT Solutions help students?
These solutions provide clear, step-by-step explanations to help students understand how to find the axes of symmetry for different figures, aiding in concept mastery and exam revision.
What is an axis of symmetry?
An axis of symmetry is a line that divides a figure into two identical halves, such that if the figure were folded along this line, the two halves would match perfectly.
Are there different types of symmetry covered in this chapter?
This chapter primarily focuses on reflectional symmetry, where a line of symmetry is identified. Other types of symmetry might be introduced in later classes.
Can I use these solutions to practice identifying symmetry?
Yes, the solutions are designed to help you practice identifying and drawing lines of symmetry for various figures presented in the exercises.
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