Master NCERT Exemplar Class 7 Maths Chapter 14 MCQ on Symmetry with detailed explanations and practice questions aligned with CBSE 2025-26 guidelines.
Chapter 14 of the NCERT Class 7 Mathematics textbook introduces students to the fascinating world of Symmetry, a concept that connects mathematics to art, nature, and everyday objects. This chapter builds upon the basic understanding of symmetry from earlier classes and explores two important types: line symmetry (also called reflectional symmetry) and rotational symmetry. Understanding these concepts is essential for developing spatial reasoning and geometric thinking skills.
The NCERT Exemplar problems for this chapter are specifically designed to test your conceptual clarity beyond routine textbook exercises. These Multiple Choice Questions challenge students to identify symmetrical properties in various figures, determine the order of rotational symmetry, and recognise patterns in letters and shapes. Regular practice with these MCQs will strengthen your problem-solving abilities and prepare you effectively for CBSE examinations.
Before attempting the quiz below, ensure you have revised the key definitions such as centre of rotation, angle of rotation, and line of symmetry. This page provides a comprehensive collection of MCQ questions that cover all important topics from Chapter 14, complete with correct answers and explanations to help you understand the reasoning behind each solution.
Understanding Symmetry Concepts for MCQ Success
The study of symmetry in Class 7 Mathematics focuses on two fundamental concepts that students must thoroughly understand to excel in the NCERT Exemplar Class 7 Maths Chapter 14 MCQ section. Line symmetry, also known as reflectional symmetry, occurs when a figure can be folded along a line such that one half exactly covers the other half. This line is called the axis of symmetry or mirror line.
Line Symmetry: A figure has line symmetry if there exists at least one line that divides it into two mirror-image halves. Common examples include the letter H (vertical line symmetry), the letter E (horizontal line symmetry), and the letter X (both vertical and horizontal line symmetry).
Rotational symmetry is the second major concept covered in this chapter. A figure has rotational symmetry if it looks exactly the same after being rotated by an angle less than 360 degrees about a fixed point called the centre of rotation. The number of times a figure coincides with its original position during a complete 360-degree rotation is called the order of rotational symmetry.
For instance, an equilateral triangle has rotational symmetry of order 3 because it looks identical at rotations of 120°, 240°, and 360°. Similarly, a square has rotational symmetry of order 4, coinciding with itself at 90°, 180°, 270°, and 360° rotations. Understanding these principles is crucial for solving MCQ questions accurately.
Why This Matters: Symmetry concepts appear frequently in competitive examinations like Olympiads and foundation courses. Mastering Chapter 14 MCQs builds the analytical thinking required for advanced geometry topics in higher classes, including transformations and coordinate geometry.
Students preparing for their annual examinations should pay special attention to questions involving English alphabet letters and their symmetry properties. Many MCQs test whether students can identify letters with vertical mirror symmetry (A, H, I, M, O, T, U, V, W, X, Y), horizontal mirror symmetry (B, C, D, E, H, I, K, O, X), or both types of symmetry (H, I, O, X). For comprehensive practice across different mathematical chapters, you can also explore NCERT Exemplar Class 11 Maths Chapter 1 MCQ to understand how these concepts evolve in higher classes.
Key Formulas and Concepts for Solving Symmetry MCQs
Success in the NCERT Exemplar Class 7 Maths Chapter 14 MCQ section requires a solid grasp of several important formulas and relationships. The angle of rotation for a figure with rotational symmetry of order n can be calculated using a simple formula that every student should memorise.
Angle of Rotation Formula: If a figure has rotational symmetry of order n, then the angle of rotation = 360° ÷ n. For example, a regular hexagon (order 6) has an angle of rotation of 360° ÷ 6 = 60°.
When solving MCQ questions about regular polygons, remember that every regular polygon has both line symmetry and rotational symmetry. A regular polygon with n sides has exactly n lines of symmetry and rotational symmetry of order n. This relationship is fundamental to answering questions about squares, equilateral triangles, regular pentagons, and hexagons.
The table below summarises the symmetry properties of common geometric shapes that frequently appear in NCERT Exemplar MCQs. Understanding these properties will help you quickly identify correct answers without lengthy calculations.
| Class | Subject | Total Questions | Total Units | Link |
|---|---|---|---|---|
| Class VI | Mathematics | 319 | 25 | View → |
| Class VII | Mathematics | 600 | 19 | View → |
| Class VIII | Mathematics | 740 | 31 | View → |
| Class IX | Mathematics | 1,638 | 33 | View → |
| Class X | Mathematics | 1,944 | 34 | View → |
| Class XI | Mathematics | 857 | 38 | View → |
| Class XII | Mathematics | 788 | 56 | View → |
Another important concept tested in Chapter 14 MCQs involves identifying figures that possess no line of symmetry but have rotational symmetry. The parallelogram is a classic example—it has rotational symmetry of order 2 but no line of symmetry. Similarly, the letter S has rotational symmetry of order 2 but no axis of symmetry. These distinctions are frequently tested in CBSE examinations.
Important: Do not confuse the number of lines of symmetry with the order of rotational symmetry. While they are equal for regular polygons, this relationship does not hold for all figures. For instance, a rectangle has 2 lines of symmetry and rotational symmetry of order 2, but an isosceles triangle has only 1 line of symmetry and no rotational symmetry (order 1 is considered trivial).
Students should also practice identifying the centre of rotation in various figures. For regular polygons, the centre of rotation is the geometric centre (centroid). For letters and irregular figures, you must carefully observe which point remains fixed during rotation. Questions asking you to identify the centre marked with ‘x’ in a figure are common in the Exemplar book.
Effective Practice Strategies for Symmetry MCQ Questions
Developing a systematic approach to solving NCERT Exemplar Class 7 Maths Chapter 14 MCQ questions can significantly improve your accuracy and speed. The first strategy involves visual verification—before selecting an answer, mentally rotate or fold the figure to confirm your choice. This habit prevents careless mistakes that often occur when students rush through objective questions.
For questions about reflectional symmetry in letters, use the mirror test method. Imagine placing a vertical or horizontal mirror along the potential axis of symmetry. If the reflection matches the original letter, symmetry exists. This technique is particularly useful for letters like B (horizontal symmetry only), A (vertical symmetry only), and H (both symmetries).
Why This Matters: The CBSE examination pattern increasingly includes competency-based questions that require application of concepts rather than mere recall. Practising with Exemplar MCQs trains you to think critically and apply symmetry principles to unfamiliar figures and situations.
When determining the order of rotational symmetry, use the tracing paper method. Trace the figure on transparent paper, place a pin at the centre of rotation, and count how many times the traced figure coincides with the original during one complete rotation. This practical approach helps verify theoretical answers and builds intuition for symmetry problems.
Time management is crucial when attempting MCQ sections. Allocate approximately 1-2 minutes per question during practice sessions. If a question seems complex, mark it for review and move forward—returning with fresh perspective often reveals the solution. The MCQ quiz provided on this page follows the same difficulty level as questions published by NCERT on their official website ncert.nic.in.
Consider creating flashcards for English letters organised by their symmetry properties. One card might list all letters with vertical symmetry, another with horizontal symmetry, and a third with both. Regular review of these cards ensures quick recall during examinations. Students aiming for higher classes can benefit from exploring NCERT Exemplar Class 11 Maths Chapter 14 MCQ to see how probability concepts connect with logical reasoning skills developed through symmetry studies.
Common Mistakes to Avoid in Chapter 14 MCQ Examinations
Understanding common errors helps students avoid losing marks on questions they actually know. The most frequent mistake in NCERT Exemplar Class 7 Maths Chapter 14 MCQ involves confusing line symmetry with rotational symmetry. Remember that these are independent properties—a figure may have one, both, or neither type of symmetry.
Another common error occurs when students miscount the order of rotational symmetry. Every figure has at least order 1 (a complete 360° rotation always returns it to the original position), but mathematically meaningful rotational symmetry requires order 2 or higher. When a question asks if a figure has rotational symmetry, they typically mean order greater than 1.
Important: Pay careful attention to whether questions ask about capital letters or lowercase letters. The symmetry properties differ significantly. For example, capital B has horizontal symmetry, but lowercase b has no line symmetry. Always assume capital letters unless specifically stated otherwise.
Students often make mistakes with quadrilaterals by assuming all four-sided figures share similar symmetry properties. This is incorrect. A square has 4 lines of symmetry and order 4 rotational symmetry. A rectangle has only 2 lines of symmetry and order 2 rotational symmetry. A parallelogram has no lines of symmetry but has order 2 rotational symmetry. A trapezium (in general) has neither line symmetry nor rotational symmetry of order greater than 1.
When identifying the centre of rotation from a diagram, students sometimes select a vertex instead of the central point. The centre of rotation is always the point that remains stationary during rotation—for most regular figures, this is the geometric centre, not any corner or edge point. Carefully observe the ‘x’ or dot marked in the figure before answering.
A conceptual mistake involves the isosceles triangle. While it has 1 line of symmetry (the altitude from the vertex angle to the base), it does not have rotational symmetry of order greater than 1. Only equilateral triangles among triangles possess meaningful rotational symmetry (order 3). For additional practice with geometric concepts, the NCERT Exemplar Class 11 Maths Chapter 11 MCQ on Conic Sections builds upon spatial reasoning skills.
Finally, remember that the order of rotational symmetry for a circle is infinite, as it looks identical at every angle of rotation. However, practical MCQ questions rarely ask about circles directly—they may instead ask about circular objects with patterns or markings that reduce the symmetry order.