How many practice questions are available for Symmetry?

SparkEd Math offers 60+ practice questions for Symmetry across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Symmetry content free on SparkEd Math?

Yes! All Symmetry content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Symmetry differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Symmetry problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Symmetry content aligned with the Olympiad syllabus?

Yes, all Symmetry questions and lessons on SparkEd Math are fully aligned with the Mathematical Olympiad Preparation (Olympiad) syllabus for Class 6. The content follows the official curriculum structure and exam pattern.

Symmetry — Class 6 Olympiad (2025-26)

About Symmetry — Class 6 Olympiad

Identify lines of symmetry, rotational symmetry, and solve mirror image and figure completion puzzles. This topic is part of the Olympiad Class 6 mathematics syllabus (chapter: Module 11). On this page you can practice 59 questions across three difficulty levels — 19 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.

Symmetry — solved examples for Class 6 Olympiad

Example 1easy

How many lines of symmetry does a regular pentagon have?

Step-by-step solution

A regular polygon has a number of lines of symmetry equal to its number of sides.
A pentagon is a polygon with 5 sides.
Since it is a regular pentagon, each vertex and the midpoint of each opposite side will define a line of symmetry. There are 5 such lines.

Answer: 5

Example 2medium

A square has all its four corners cut off by identical, small, isosceles right-angled triangles such that the resulting figure is a regular octagon. How many lines of symmetry does this regular octagon have?

A)A) 4
B)B) 8
C)C) 2
D)D) 0

Step-by-step solution

When a square's four corners are cut off by identical, small, isosceles right-angled triangles, and the resulting figure is a regular octagon.
A regular polygon with 'n' sides has exactly 'n' lines of symmetry.
Since the resulting figure is a regular octagon, it has 8 sides.
Therefore, the regular octagon has 8 lines of symmetry.

Answer: B) 8

Example 3hard

A decorative lamp shade is constructed by joining 8 identical isosceles triangles around a central point. Each triangle has its unique pattern. The entire lampshade is designed such that it looks exactly the same only when rotated by multiples of 45°. However, if we draw a line through the center of the lampshade, it never divides the lampshade into two identical mirror halves. Which of the following statements about the lampshade is true?

A)It has 8 lines of symmetry and rotational symmetry of order 8.
B)It has no lines of symmetry but has rotational symmetry of order 8.
C)It has 4 lines of symmetry and rotational symmetry of order 4.
D)It has no lines of symmetry and no rotational symmetry of order greater than 1.

Step-by-step solution

The problem states that the lampshade looks exactly the same when rotated by multiples of 45°. Since 360° / 45° = 8, this means it has rotational symmetry of order 8.
The problem also states that 'if we draw a line through the center of the lampshade, it never divides the lampshade into two identical mirror halves.' This directly indicates that the lampshade has no lines of symmetry.
Combining these two facts, the lampshade has no lines of symmetry but has rotational symmetry of order 8.
This matches option B.

Answer: It has no lines of symmetry but has rotational symmetry of order 8.

Practice questions on Symmetry

Q1.easy
Which of the following capital English letters has exactly two lines of symmetry, one horizontal and one vertical?
1. A)A
2. B)H
3. C)E
4. D)X
Show answer
Answer: H
Hint: Visualize folding each letter along its horizontal and vertical midlines to see if the halves match perfectly.
Q2.easy
A figure can be rotated by 90°, 180°, 270°, and 360° about its center to look exactly the same as its original position. What is the order of rotational symmetry of this figure?
1. A)2
2. B)3
3. C)4
4. D)5
Show answer
Answer: 4
Hint: The order of rotational symmetry is the number of times a figure looks identical during a full 360° rotation (excluding the 360° rotation itself, which always matches).
Q3.easy
A line L is the line of symmetry for a figure. If point A is on one side of L, and point B is its image after reflection across L, where would the midpoint of the segment AB lie?
1. A)On point A
2. B)On point B
3. C)On the line L
4. D)Outside the segment AB
Show answer
Answer: On the line L
Hint: Recall the definition of a line of symmetry. It acts like a perpendicular bisector for any segment connecting a point to its reflected image.
Q4.medium
What is the order of rotational symmetry of the capital letter 'N'?
1. A)A) 1
2. B)B) 2
3. C)C) 3
4. D)D) 4
Show answer
Answer: B) 2
Hint: Visualize rotating the letter around its center point. How many times does it look identical to the original within a full 360° turn?
Q5.medium
A clock shows the time 3:30. If this clock is viewed in a plane mirror, what time will the mirror image appear to show?
1. A)A) 8:30
2. B)B) 9:30
3. C)C) 8:00
4. D)D) 9:00
Show answer
Answer: A) 8:30
Hint: For a clock's mirror image, a common trick is that the sum of the actual time and the mirror time often adds up to 12:00 or 11:60.
Q6.medium
A figure's left half is given as a semi-circle with its diameter on the vertical axis. If the figure has vertical line symmetry, what will be the complete figure?
1. A)A) A full circle
2. B)B) A semi-circle
3. C)C) A square
4. D)D) A triangle
Show answer
Answer: A) A full circle
Hint: A vertical line of symmetry means the right half is an exact mirror image of the left half across the vertical line.
Q7.hard
A special 10-digit digital clock display, where each digit (0-9) is represented by a unique block pattern, shows the time '08:08'. If this display is viewed through a mirror placed horizontally below it, how many of the displayed digits will appear exactly the same as their original form?
1. A)0
2. B)2
3. C)3
4. D)4
Show answer
Answer: 2
Hint: Consider the horizontal line of symmetry for each digit. Only digits with a horizontal line of symmetry will appear the same when reflected horizontally.
Q8.hard
Consider a figure made by arranging 6 identical equilateral triangles around a common vertex, forming a regular hexagon. Now, place a small dot in the exact center of only three alternate triangles. How many lines of symmetry does this new figure possess?
1. A)0
2. B)2
3. C)3
4. D)6
Show answer
Answer: 3
Hint: Visualize the arrangement. The dots break some symmetries. Consider lines passing through the center and vertices/midpoints.
Q9.hard
A specific type of 7-segment display shows the digit '2'. If this display is rotated 180° about its center, which digit, if any, will it appear to be?
1. A)2
2. B)5
3. C)S
4. D)None of the above
Show answer
Answer: None of the above
Hint: Sketch the digit '2' on a 7-segment display. Then visualize how each segment would move when rotated 180°.

These are 9 of the 59 questions available for Symmetry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.