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About Symmetry — Class 7 ICSE

Explore rotational symmetry and lines of symmetry in regular polygons. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 13). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Symmetry

  • Introduction to Lines of Symmetry
  • Lines of Symmetry in Regular Polygons
  • Introduction to Rotational Symmetry
  • Rotational Symmetry in Regular Polygons
  • Combined Symmetries and Lesson Summary

Interactive lesson · about 15 minutes · checkpoint question after every unit

Symmetry — solved examples for Class 7 ICSE

Example 1easy

Which of the following statements correctly defines a line of symmetry for a 2D shape?
  1. A)It is a line that passes through the centre of the shape.
  2. B)It is a line that divides the shape into two parts of equal area.
  3. C)It is a line along which a shape can be folded so that both halves match exactly.
  4. D)It is a line that connects two opposite vertices of the shape.

Step-by-step solution

  1. A line of symmetry is essentially a line of reflection.
  2. When a shape is folded along its line of symmetry, the two resulting halves perfectly superimpose each other. This means they are mirror images.

Answer: It is a line along which a shape can be folded so that both halves match exactly.

Example 2medium

Which of the following statements about a line of symmetry is INCORRECT?
  1. A)A) A line of symmetry divides a figure into two identical halves.
  2. B)B) The two halves of a figure on either side of a line of symmetry are mirror images of each other.
  3. C)C) A line of symmetry must always pass through the centre of the figure.
  4. D)D) A figure can have multiple lines of symmetry.

Step-by-step solution

  1. A line of symmetry reflects one half of a figure onto the other, meaning they are identical mirror images. So, options A and B are correct statements.
  2. Many figures, like a square or an equilateral triangle, have multiple lines of symmetry. So, option D is a correct statement.
  3. However, a line of symmetry does not *always* pass through the geometric centre. For example, in an isosceles triangle, the line of symmetry passes through one vertex and the midpoint of the opposite side, but this line does not pass through the centroid (geometric center) unless the triangle is equilateral. Thus, statement C is incorrect.

Answer: C) A line of symmetry must always pass through the centre of the figure.

Example 3hard

A geometric figure has rotational symmetry of order 2 but does not have any line of symmetry. Which of the following figures could it be?
  1. A)Rectangle
  2. B)Rhombus
  3. C)Parallelogram
  4. D)Square

Step-by-step solution

  1. A rectangle has 2 lines of symmetry and rotational symmetry of order 2.
  2. A rhombus has 2 lines of symmetry and rotational symmetry of order 2.
  3. A square has 4 lines of symmetry and rotational symmetry of order 4.
  4. A parallelogram (that is not a rectangle or a rhombus) has rotational symmetry of order 2 (about its center) but does not have any line of symmetry. It only looks the same after a 180° rotation, but cannot be folded to get a mirror image.

Answer: Parallelogram

Practice questions on Symmetry

  1. Q1.easy

    How many lines of symmetry does a regular pentagon have?
    1. A)3
    2. B)4
    3. C)5
    4. D)6
    Show answer

    Answer: 5

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

  2. Q2.easy

    Which of the following capital letters has exactly two lines of symmetry?
    1. A)A
    2. B)S
    3. C)H
    4. D)E
    Show answer

    Answer: H

    Hint: Visualize folding each letter both horizontally and vertically.

  3. Q3.easy

    The 'order' of rotational symmetry of a shape is the number of times it looks exactly the same during a full rotation of 360° around its centre. Based on this, what is the order of rotational symmetry for a square?
    1. A)1
    2. B)2
    3. C)3
    4. D)4
    Show answer

    Answer: 4

    Hint: Imagine rotating a square. How many times does it align perfectly with its original position before completing a full 360° turn?

  4. Q4.medium

    How many lines of symmetry does the English alphabet letter 'Z' have when written in a standard block capital form?
    1. A)A) 0
    2. B)B) 1
    3. C)C) 2
    4. D)D) 4
    Show answer

    Answer: A) 0

    Hint: Try visualizing or drawing lines through the letter 'Z'. Would both halves perfectly overlap or be mirror images if folded along any line?

  5. Q5.medium

    A rhombus is a quadrilateral with all four sides equal in length. How many lines of symmetry does a rhombus (that is not a square) have?
    1. A)A) 0
    2. B)B) 1
    3. C)C) 2
    4. D)D) 4
    Show answer

    Answer: C) 2

    Hint: Consider the special lines within a rhombus, such as its diagonals. Do they act as lines of symmetry?

  6. Q6.medium

    A traditional Indian rangoli design is created using a pattern that is identical when viewed from four different directions after rotation by 90°. If this rangoli also has reflective symmetry along a horizontal line and a vertical line, how many lines of symmetry does the complete design possess?
    1. A)A) 2
    2. B)B) 4
    3. C)C) 6
    4. D)D) 8
    Show answer

    Answer: B) 4

    Hint: If a figure has rotational symmetry of order 'n' and also possesses at least one line of symmetry, it will have 'n' lines of symmetry in total.

  7. Q7.hard

    If a regular polygon has 9 lines of symmetry, what is the measure of each of its interior angles?
    1. A)120°
    2. B)140°
    3. C)150°
    4. D)160°
    Show answer

    Answer: 140°

    Hint: For a regular polygon, the number of lines of symmetry is equal to the number of its sides. Use this information to find the number of sides, and then calculate the interior angle.

  8. Q8.hard

    A student calculated the angle of rotational symmetry for a regular hexagon as 90°. Which of the following statements correctly identifies the student's mistake?
    1. A)A hexagon does not have rotational symmetry.
    2. B)The student confused the angle of rotational symmetry with the interior angle of a square.
    3. C)The student should have divided 360° by 4, not 6.
    4. D)The correct angle of rotational symmetry for a regular hexagon is 60°.
    Show answer

    Answer: The student should have divided 360° by 4, not 6.

    Hint: Recall the formula for the angle of rotational symmetry for a regular polygon (360° / number of sides). What number, when divided into 360°, gives 90°? How does that relate to a hexagon?

  9. Q9.hard

    Two identical equilateral triangles are joined together by matching one full side of each. The resulting figure is a rhombus. Which of the following correctly describes the symmetries of this rhombus?
    1. A)2 lines of symmetry and order 2 rotational symmetry.
    2. B)4 lines of symmetry and order 2 rotational symmetry.
    3. C)2 lines of symmetry and order 4 rotational symmetry.
    4. D)4 lines of symmetry and order 4 rotational symmetry.
    Show answer

    Answer: 2 lines of symmetry and order 2 rotational symmetry.

    Hint: Visualize the rhombus formed by the two equilateral triangles. Remember that a rhombus has specific properties, and it's not always a square. Consider how many ways you can fold it symmetrically and how many times it looks identical when rotated within a full turn.

These are 9 of the 60 questions available for Symmetry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.