This MCQ module is based on: Line Symmetry and Mirror Reflection
TOPIC 33 OF 41
Line Symmetry and Mirror Reflection
🎓 Class 6
Mathematics
CBSE
Theory
Ch 9 — Symmetry
⏱ ~30 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Line Symmetry and Mirror Reflection
Targeting Class 6 level in Geometry, with Basic difficulty.
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9.1 Symmetry All Around Us
Look around — flowers, butterflies, a rangoli, a pinwheel, the Taj Mahal, temple gopurams. Many beautiful objects share a common feature: parts of the figure repeat in a definite pattern. This pleasing regularity is called symmetry?.
Definition
A figure has symmetry when a part (or parts) of it repeats in a definite pattern. A pinwheel, for example, looks the same when rotated, while a butterfly looks the same across a central line.Not every figure is symmetric. Clouds, an irregular stone, or a splash of water do not repeat in a fixed pattern — they are non-symmetric.
Symmetric figures repeat in a definite pattern; clouds do not.
9.2 Line of Symmetry
Fold a figure along a line. If the two halves match completely — coinciding point for point — then the figure has line symmetry?. The fold line is called the line of symmetry (or axis of symmetry, or mirror line).
Definition
A figure has line symmetry if there is a straight line along which the figure can be folded so that the two halves overlap exactly. That line is called the line of symmetry.Example 1 — The English Letter "A"
The capital letter A can be folded down the middle — the left half mirrors the right. So A has one vertical line of symmetry.
Letter A (1 line), Square (4 lines), Rectangle (2 lines)
🔵 Try it: Which English capital letters have at least one line of symmetry? A, B, C, D, E, H, I, K, M, O, T, U, V, W, X, Y — these 17 letters are line-symmetric. F, G, J, L, N, P, Q, R, S, Z have none.
Figures with Multiple Lines of Symmetry
Some figures have more than one line of symmetry.
- Equilateral triangle → 3 lines (one through each vertex and the opposite side's midpoint).
- Square → 4 lines (2 through midpoints of opposite sides + 2 diagonals).
- Regular hexagon → 6 lines.
- Circle → infinite lines (every diameter is a line of symmetry).
🔵 Is the diagonal of a rectangle a line of symmetry? Fold a rectangle along its diagonal — the two halves do not coincide (the sides have different lengths). So a rectangle's diagonals are not lines of symmetry. But for a square, they are.
9.3 Reflection — How the Mirror Line Works
When a figure has a line of symmetry, one half is the mirror reflection of the other. Mathematicians use this idea:
Key Idea — Reflection
If P is any point on one side of the line of symmetry, then its reflection P' (read "P prime") lies on the other side, such that:(i) The line joining P and P' is perpendicular to the line of symmetry.
(ii) P and P' are at equal distances from the line of symmetry.
Reflection: perpendicular distance on each side must be equal.
Activity: Ink-Fold Symmetry
L3 ApplyMaterials: Paper, washable ink / watercolour, brush
Predict: If you drop ink on half a folded paper and press the halves together, what kind of shape appears when you open it?
- Fold a rectangular sheet of paper in half. Unfold it — the crease is your line of symmetry.
- On one half only, drop a few blobs of ink or watercolour.
- Fold the paper quickly along the crease and press gently.
- Open it. Observe the image.
Observation: Every blob has an exact mirror partner on the other half. The crease is the line of symmetry. This is how we verify line symmetry physically — a paper fold test.
Figure it Out — Part A
Q1. Which of the shapes below have a line of symmetry? For the symmetric ones, draw the line(s).
Equilateral triangle → 3 lines. Rectangle → 2 lines. Isosceles triangle → 1 line. Scalene triangle → 0 lines. Circle → infinite. Regular pentagon → 5 lines.
Q2. Complete each figure so that the dashed line becomes a line of symmetry: (i) a half of a heart, (ii) a half of an arrow.
Reflect every corner/point of the given half across the dashed line at the same perpendicular distance. Join the reflected points in the same order — the completed figure is symmetric about the dashed line.
Q3. Does the diagonal of a rhombus (where all four sides are equal) act as a line of symmetry? Justify.
Yes. Folding a rhombus along a diagonal makes the two triangular halves coincide, because the four sides are equal and the diagonal bisects both pairs of opposite angles. A rhombus has 2 lines of symmetry — both its diagonals.
Historical Note
Indian rangoli (also called kolam in Tamil Nadu, muggu in Andhra, alpana in Bengal) has used symmetry for over 5,000 years. A rangoli designer mentally reflects a pattern across multiple axes — a deep application of line and rotational symmetry in daily Indian life.Competency-Based Questions
Scenario: Aarti is designing a kite-shaped logo for her school's art club. Her first sketch shows the outline ABCD with AB = AD = 6 cm and CB = CD = 9 cm, and the diagonal AC drawn in.
Q1. Identify all lines of symmetry in Aarti's kite ABCD. Explain.
L3 ApplyAnswer: The diagonal AC is the only line of symmetry, because folding along AC makes side AB coincide with AD and CB with CD. The other diagonal BD is not an axis because AB ≠ CB. So a kite has exactly 1 line of symmetry.
Q2. Aarti's friend says, "Every quadrilateral with two pairs of equal adjacent sides must have at least one line of symmetry." Analyse whether this claim is always true.
L4 AnalyseAnswer: True — a kite (AB=AD and CB=CD) always has symmetry along the diagonal joining the two "unequal-neighbour" vertices (A and C). The two halves fold onto each other perfectly. So the claim holds.
Q3. A school badge must have at least 4 lines of symmetry. Evaluate which of these base shapes satisfy the rule: (a) rhombus, (b) rectangle, (c) square, (d) regular hexagon, (e) equilateral triangle.
L5 EvaluateAnswer: (a) rhombus — 2 ✗ (b) rectangle — 2 ✗ (c) square — 4 ✓ (d) regular hexagon — 6 ✓ (e) equilateral triangle — 3 ✗. Only square and regular hexagon qualify.
Q4. Create a new 8-point star logo (like a rangoli) that has exactly 8 lines of symmetry. Describe how you would draw it.
L6 CreateSample design: Draw a circle. Mark 8 equally-spaced points around it (every 45°). Join each point to its 3rd neighbour to make a star. All 8 lines from centre through each point (and between adjacent points) are lines of symmetry. This 8-pointed star has exactly 8 axes.
Assertion–Reason Questions
Assertion (A): A circle has infinitely many lines of symmetry.
Reason (R): Every diameter of a circle divides it into two equal halves that coincide when folded.
Reason (R): Every diameter of a circle divides it into two equal halves that coincide when folded.
(a) Every diameter acts as an axis, and a circle has infinitely many diameters.
Assertion (A): A rectangle has 4 lines of symmetry.
Reason (R): A rectangle has two pairs of equal opposite sides.
Reason (R): A rectangle has two pairs of equal opposite sides.
(d) A is false — a rectangle has only 2 lines of symmetry (the two lines through midpoints of opposite sides). Its diagonals are not axes. R is a true statement but does not imply 4 axes.
Assertion (A): If P' is the reflection of P across a line ℓ, then PP' is perpendicular to ℓ and ℓ bisects PP'.
Reason (R): Reflection preserves distances from the mirror line.
Reason (R): Reflection preserves distances from the mirror line.
(a) This is precisely the geometric definition of reflection, and R is the property that makes it true.
Frequently Asked Questions
What is line symmetry?
Line symmetry means a figure can be folded along a straight line so both halves match exactly. That fold line is called the line of symmetry or mirror line.
How many lines of symmetry does a rectangle have?
A rectangle has exactly 2 lines of symmetry - one horizontal and one vertical through the centre. Its diagonals are NOT lines of symmetry.
Does the letter A have line symmetry?
Yes. Capital letter A has one vertical line of symmetry through the middle. The left half is a mirror image of the right half.
Which English capital letters have a horizontal line of symmetry?
Letters B, C, D, E, H, I, K, O, X have a horizontal line of symmetry. Fold them top-to-bottom and both halves match.
How do you test for line symmetry?
Use the paper fold test: fold the figure along the suspected line; if both halves coincide point by point, that line is a line of symmetry.
Is a scalene triangle symmetric?
No. A scalene triangle has no line of symmetry because all three sides are of different lengths, so no fold makes the halves match.
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