Class 6 Maths · Original EZT practice
Symmetry (Class 6 Chapter 9): summary and practice
A butterfly, a leaf, a rangoli. Symmetry is balance: one half matches the other. Chapter 9 covers two kinds - line symmetry and rotational symmetry. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 6). Older Class 6 books numbered chapters differently - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Line of symmetry
A shape has a line of symmetry if folding along that line makes the two halves fit exactly on each other. Some shapes have none, some one, some many.
2. Letters and everyday shapes
Test a figure by folding or using a mirror along the line. Letters A, M, T and U have a vertical line; B, C, D and E have a horizontal line; H and O have both.
3. Rotational symmetry
A figure has rotational symmetry if it looks the same after turning less than a full turn about a fixed point (the centre). The number of times it fits during one full turn is its order. A square fits at quarter turns, so its order is four.
4. Putting both together
A shape can have line symmetry, rotational symmetry, both or neither. A regular polygon with n sides has n lines of symmetry and rotational order n.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Count the lines of symmetry of a rectangle
Choose the method: Try folding along candidate lines and check whether the halves match.
EZT practice question
How many lines of symmetry does a rectangle (not a square) have?
Show the worked solution
- Fold along the vertical line through the centre - halves match.
- Fold along the horizontal line through the centre - halves match.
- Fold along a diagonal - the halves do NOT match.
Answer: Two - one vertical and one horizontal through the centre. The diagonals are not lines of symmetry.
Check: Each accepted line must make the two halves fit exactly.
Watch for this: Do not count the diagonals; on a plain rectangle the diagonal fold does not match.
Now try it yourself
How many lines of symmetry does an equilateral triangle have?
Check your answer
Three.
One line runs from each corner to the mid-point of the opposite side.
Count the lines of symmetry of a square
Choose the method: Check mid-point lines and diagonals separately.
EZT practice question
How many lines of symmetry does a square have?
Show the worked solution
- Two lines through opposite mid-points of sides work.
- Both diagonals also work for a square.
Answer: Four - two through the mid-points of opposite sides and two diagonals.
Check: All four folds make the halves fit exactly.
Watch for this: Do not stop at two; unlike a plain rectangle, a square's diagonals do work.
Now try it yourself
How many lines of symmetry does a circle have?
Check your answer
Infinitely many.
Every diameter folds the circle onto itself.
Test a letter for line symmetry
Choose the method: Imagine a mirror first vertical, then horizontal, along the letter.
EZT practice question
Does the letter H have line symmetry?
Show the worked solution
- A vertical line through the middle: left half mirrors the right.
- A horizontal line through the middle: top half mirrors the bottom.
Answer: Yes - H has both a vertical and a horizontal line of symmetry.
Check: Both mirror tests succeed.
Watch for this: Do not stop after finding one line; check the other direction too.
Now try it yourself
Name two letters with a vertical line of symmetry.
Check your answer
Any two of A, M, T, U (H and O also qualify).
Their left and right halves are mirror images.
Show a letter with no line of symmetry
Choose the method: Try both mirror directions and check each fails.
EZT practice question
Does the letter F have any line of symmetry?
Show the worked solution
- Vertical line: the arms point one way, so the halves do not match.
- Horizontal line: the top arm is longer than the bottom arm, so no match.
Answer: No - F has no line of symmetry.
Check: Both possible mirror directions fail.
Watch for this: Do not assume every capital letter is symmetric; test each one.
Now try it yourself
Does the letter S have a line of symmetry?
Check your answer
No.
No fold makes the two halves of S fit on each other.
Find the smallest turn of a square
Choose the method: Divide a full turn by the order of rotational symmetry.
EZT practice question
What is the smallest turn that brings a square back to its place?
Show the worked solution
- A square fits onto itself four times in one full turn - order four.
- Divide a full turn into four equal parts.
- Three hundred sixty degrees divided by four is ninety degrees.
Answer: Ninety degrees - a quarter turn.
Check: Four quarter turns complete one full turn, matching order four.
Watch for this: Do not answer half a turn; the square already matches at a quarter turn.
Now try it yourself
What is the order of rotational symmetry of a rectangle?
Check your answer
Two - smallest turn one hundred eighty degrees.
A rectangle matches itself only at half turns.
Find the smallest turn of an equilateral triangle
Choose the method: Divide a full turn by the order.
EZT practice question
An equilateral triangle has order three. What is its smallest turn?
Show the worked solution
- Order three means it matches itself three times per full turn.
- Three hundred sixty degrees divided by three is one hundred twenty degrees.
Answer: One hundred twenty degrees.
Check: Three turns of one hundred twenty degrees make one full turn.
Watch for this: Do not divide by the number of vertices guessed wrongly; use the order given.
Now try it yourself
What is the smallest turn for a figure of order six?
Check your answer
Sixty degrees.
Three hundred sixty divided by six is sixty.
Give lines and order for a regular hexagon
Choose the method: For a regular polygon, lines of symmetry and rotational order both equal the number of sides.
EZT practice question
A regular hexagon: how many lines of symmetry and what rotational order?
Show the worked solution
- A regular hexagon has six sides.
- Regular polygons have as many lines of symmetry as sides.
- The rotational order also equals the number of sides.
Answer: Six lines of symmetry; order six; smallest turn sixty degrees.
Check: Both counts equal the side count, as the regular-polygon rule says.
Watch for this: Do not give different numbers for lines and order on a regular polygon.
Now try it yourself
A regular pentagon: lines and smallest turn?
Check your answer
Five lines; smallest turn seventy-two degrees.
Order five, and three hundred sixty divided by five is seventy-two.
Find a shape with neither kind of symmetry
Choose the method: Check folds first, then turns, for a shape with all sides different.
EZT practice question
What symmetry does a scalene triangle have?
Show the worked solution
- All three sides are different, so no fold matches the halves.
- It matches itself only after a full turn.
- So it has neither line symmetry nor rotational symmetry.
Answer: No lines of symmetry and no rotational symmetry - only a full turn brings it back.
Check: Both tests fail, which is allowed: a shape can have neither kind.
Watch for this: Do not assume every triangle has a line of symmetry; only isosceles and equilateral ones do.
Now try it yourself
Give a shape with line symmetry but no rotational symmetry.
Check your answer
An isosceles triangle.
It has one fold line, but it matches itself only after a full turn.
Try a mixed set
Choose a method or explanation before opening each answer.
1. What is a line of symmetry?
Show answer and reason
A line along which a shape can be folded so both halves match exactly.
The fold test is the chapter's definition.
2. How many lines of symmetry does a square have?
Show answer and reason
Four.
Two mid-point lines and two diagonals.
3. What is the order of rotational symmetry?
Show answer and reason
The number of times a figure matches itself in one full turn.
A square has order four.
4. How do you find the smallest turn?
Show answer and reason
Divide three hundred sixty degrees by the order.
For a square, three hundred sixty divided by four is ninety degrees.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Find three objects at home that have a line of symmetry and name the line.
- Sort the letters of your name into symmetric and not symmetric.
- A figure matches itself five times in one full turn - what is its smallest turn?
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Questions about this practice page
- What is a line of symmetry?
- A line along which a shape can be folded so both halves match exactly.
- How many lines of symmetry does a square have?
- Four - two through the mid-points of opposite sides and two diagonals.
- What is the order of rotational symmetry?
- The number of times a figure matches itself in one full turn.
- How do I find the smallest turn?
- Divide three hundred sixty degrees by the order - for a square, three hundred sixty divided by four is ninety degrees.
- Are these the NCERT exercise questions for Symmetry?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.