MathsICSE Class 8 · Symmetry

Lines of Symmetry and Reflection (ICSE Class 8 Maths)

Updated 17 October 2026 · Fact-checked

A figure has reflection symmetry if a line (the line of symmetry) splits it into two halves that are mirror images. A regular polygon with $n$ sides has $n$ lines of symmetry. In a reflection, every point and its image are the same perpendicular distance from the mirror line, on opposite sides.

Each point and its image lie on a line perpendicular to the mirror, at equal distance d on opposite sides, so the image has the same size and shape.

Illustration drawn for QuestionBuddy.

Understand Lines of Symmetry and Reflection

The CISCE curriculum includes the idea of reflection symmetry and symmetrical shapes.

Line of symmetry. If you fold a figure along a line and the two parts fit exactly, that line is a line of symmetry (axis of symmetry).

Common shapes.

Shape	Lines of symmetry
Scalene triangle	0
Isosceles triangle	1
Equilateral triangle	3
Parallelogram (not a rectangle or rhombus)	0
Rectangle	2
Rhombus	2
Kite	1
Square	4
Regular $n$ -gon	$n$
Circle	infinitely many

Letters. In block capitals, A, M, T, U, V, W, Y have one vertical line; B, C, D, E, K have one horizontal line; H, I, O, X have two (or more); F, G, J, L, N, P, Q, R, S, Z have none.

Reflection in a mirror line. The image of a point is at the same perpendicular distance from the mirror, on the other side. So a point at distance $d$ from the mirror is $2 d$ from its image. The image has the same size and shape as the original, with left and right reversed.

Regular polygons. A regular $n$ -gon has $n$ lines of symmetry, exterior angle $\frac{36 0 ^{\circ}}{n}$ , interior angle $18 0^{\circ} - \frac{36 0 ^{\circ}}{n}$ , and the lines pass through the centre.

Using symmetry to reason. If a figure has a line of symmetry, equal sides and angles occur in pairs: this is why the base angles of an isosceles triangle are equal.

Lines of Symmetry and Reflection: formulas to remember

Regular polygon lines: $lines of symmetry = n$; For n equal sides and angles.
Exterior and interior angle: $exterior = \frac{36 0 ^{\circ}}{n}, interior = 18 0^{\circ} - \frac{36 0 ^{\circ}}{n}$; Regular n-gon.
Distance to the image: $P P^{'} = 2 d$; $d$ is the distance of $P$ from the mirror.

How to solve Lines of Symmetry and Reflection questions

Look for a fold that makes the two parts match exactly.

1Imagine folding the shape along each candidate line.
2Count the lines for which both halves coincide.
3For a reflection, drop a perpendicular from each point to the mirror and extend it by the same length.
4For regular polygons use the $n$ lines rule and the angle formulas.
5Check that the image has the same size and shape.

Lines of Symmetry and Reflection in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Reflection in a lake

Suppose a tree tip is 12 m above a calm lake surface, so its reflection appears as far below the surface.

How far apart are the tree tip and its reflected tip?

Try it first, then show the solutionSolution

Reflection is the same distance on the other side: $12$ m below.
Distance $= 2 \times 12 = 24$ m.

Answer: 24 m.

Memory hook: Mirror distance doubles for object and image.

Tricks to remember Lines of Symmetry and Reflection

Short memory aids. Say each one aloud once, then use it on a question the same day.

Fold test
Imagine folding along the line; if edges and corners match, it is a line of symmetry.
Use it when: Any figure.
n sides, n lines
Only regular polygons have as many lines as sides.
Use it when: Counting lines.

Lines of Symmetry and Reflection: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Regular polygon · 1 mark · MCQBoard level

A regular hexagon has how many lines of symmetry?
(a) 2 (b) 3 (c) 4 (d) 6

Try it first, then show the solutionSolution

A regular polygon with $n$ sides has $n$ lines: $n = 6$ .

Answer: (d)

Example 2: Count for shapes · 3 marks · Short answerBoard level

Write the number of lines of symmetry of: scalene triangle, isosceles triangle, equilateral triangle, rectangle, rhombus, kite, parallelogram, square.

Try it first, then show the solutionSolution

Scalene: $0$ ; isosceles: $1$ ; equilateral: $3$ .
Rectangle: $2$ ; rhombus: $2$ ; kite: $1$ .
Parallelogram: $0$ ; square: $4$ .

Answer: 0, 1, 3, 2, 2, 1, 0, 4

Example 3: Letters of a word · 3 marks · Short answerHarder board level

Find the total number of lines of symmetry in the letters of the word MATHS (block capitals, each letter separately).

Try it first, then show the solutionSolution

M: 1 (vertical). A: 1 (vertical). T: 1 (vertical).
H: 2 (vertical and horizontal). S: 0.
Total $= 1 + 1 + 1 + 2 + 0 = 5$ .

Answer: 5

Example 4: Reflection distances · 4 marks · Short answerHarder board level

A triangle $A B C$ has its vertices at distances of 2 cm, 3 cm and 5 cm from a mirror line, all on the same side. Find the distance of each vertex from its image, and the distance of each image vertex from the mirror.

Try it first, then show the solutionSolution

Each image is on the other side at the same distance: $2$ , $3$ and $5$ cm from the mirror.
Distance from vertex to image $= 2 \times$ distance: $4$ , $6$ and $10$ cm.
The image triangle is congruent to $A B C$ , with reversed orientation.

Answer: Images at 2, 3, 5 cm; A to A' = 4 cm, B to B' = 6 cm, C to C' = 10 cm.

Example 5: A regular polygon from its symmetry · 4 marks · Long answerHOTS / competency

A regular polygon has 9 lines of symmetry. Find its exterior angle, its interior angle and the sum of its interior angles.

Try it first, then show the solutionSolution

Nine lines means $n = 9$ .
Exterior angle $= \frac{360}{9} = 4 0^{\circ}$ ; interior angle $= 180 - 40 = 14 0^{\circ}$ .
Sum of interior angles $= 9 \times 140 = 126 0^{\circ}$ (check: $(9 - 2) \times 180 = 1260$ ).

Answer: $4 0^{\circ}$ ; $14 0^{\circ}$ ; $126 0^{\circ}$

Where students lose marks in Lines of Symmetry and Reflection

The slips examiners see most often, and what to write instead.

Mistake: Counting diagonals of a rectangle as lines of symmetry
Folding along a diagonal does not make the halves coincide unless the sides are equal.
Wrong working
Rectangle has 4 lines of symmetry.
Right working
Rectangle has 2.
Do this: Test by folding, not by guessing.
Usually costs: Answer mark.
Mistake: Giving the image the same distance as the object, not double, for object-image gap
The distance between a point and its image is twice its distance from the mirror.
Wrong working
Point 3 cm from the mirror is 3 cm from its image.
Right working
It is $6$ cm from its image.
Do this: Add both sides of the mirror.
Usually costs: Answer mark.

Exam tips

Use the word "congruent" for the original and its image.
Show dotted lines for the lines of symmetry.
For letters, say which orientation (block capital) you assume.

Practice questions on Lines of Symmetry and Reflection

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Which letter has no line of symmetry (block capitals)?
(a) H (b) E (c) Z (d) T
Hint
Try folding each.
Answer
(c)
Q2 · 2 marks · Short answerBoard level
State the number of lines of symmetry of an equilateral triangle, a square, a rhombus and a circle.
Hint
Remember the table.
Answer
$3$ , $4$ , $2$ and infinitely many.
Q3 · 3 marks · Short answerHarder board level
Find the total number of lines of symmetry in the letters of the word BOOK (block capitals).
Hint
B and K have horizontal lines; O has two.
Answer
B: 1, O: 2, O: 2, K: 1. Total $= 6$ .
Q4 · 3 marks · Short answerHarder board level
A triangle has vertices 1 cm, 4 cm and 6 cm from a mirror line, on the same side. Find the distance between each vertex and its image.
Hint
Twice the distance.
Answer
$2$ cm, $8$ cm and $12$ cm.
Q5 · 4 marks · Long answerHOTS / competency
A quadrilateral has exactly four lines of symmetry. Name it and find the angle between two neighbouring lines. Why can a rectangle that is not a square not have four?
Hint
Four lines through the centre divide 180 degrees equally.
Answer
It is a square. Neighbouring lines make $\frac{180}{4} = 4 5^{\circ}$ . A non-square rectangle has only the two lines that join midpoints of opposite sides; the diagonals do not fold it onto itself because adjacent sides are unequal.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Lines of symmetry of a square?Show answer
4.
2.Lines of symmetry of a parallelogram (general)?Show answer
0.
3.Distance between a point and its image if the point is 4 cm from the mirror?Show answer
8 cm.
4.Exterior angle of a regular octagon?Show answer
45 degrees.

Lines of Symmetry and Reflection (ICSE Class 8 Maths)

Understand Lines of Symmetry and Reflection

Lines of Symmetry and Reflection: formulas to remember

How to solve Lines of Symmetry and Reflection questions

Lines of Symmetry and Reflection in real life

Tricks to remember Lines of Symmetry and Reflection

Lines of Symmetry and Reflection: solved examples

Where students lose marks in Lines of Symmetry and Reflection

Exam tips

Practice questions on Lines of Symmetry and Reflection

Test your recall

Lines of Symmetry and Reflection: frequently asked questions

Does every shape have a line of symmetry?

Is the image in a mirror the same size?