What a fold line is
Fold, do not stare.
A line of symmetry is a line you can fold a figure along so that one half hides the other. Nothing may stick out anywhere. That single test decides every question in this topic.
📚 Chapter Learning Kit
Symmetry · Class 6 Mathematics · Ganita Prakash
English 5 topics 145 leveled MCQs 75 flashcards 9 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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Symmetry in one sentence
A part that returns.
A figure has symmetry when a part of it comes back again in a fixed pattern. A cloud has nothing that comes back, so a cloud is asymmetrical.
Zero fold lines is normal
None is a fine answer.
A triangle with three unequal sides cannot be folded into matching halves at all. Plenty of ordinary shapes are like that, and the drawing is not at fault.
Why a fold makes symmetry
The crease draws for you.
Press a folded sheet and every mark is copied across the crease at the same distance. The crease becomes a line of symmetry of whatever comes out.
Ink blots
Ink first, plan later.
Drop ink on one half of a folded sheet, press and open. The pattern is symmetrical about the crease, whatever shape the drop happened to make.
Cutting a folded sheet
One snip, two holes.
A cut on a folded sheet goes through every layer. Open the sheet and each layer has given you a matching piece of the hole.
📖 Smart notes
What you'll study, topic by topic
1
Lines of Symmetry
A line of symmetry is a fold line: close the paper along it and one half hides the other. Some figures fold no way at all, some fold once, and a square folds four ways.
- A line of symmetry cuts a figure into two parts that land exactly on each other when the paper is folded along it.
- A figure may have no fold line, one fold line, several, or endlessly many as a circle does.
- A square folds four ways: two lines through the middles of opposite sides and two along its diagonals.
~30 min · full explanation, examples & memory tricks in the app
2
Making Symmetric Shapes
Ink blots, paper cutting and a hole punch all build symmetry the same way. A fold copies one side onto the other, so the crease becomes a line of symmetry of whatever you make.
- Pressing a folded sheet copies every mark across the crease, so the crease becomes a line of symmetry.
- A cut made on a folded sheet is really a cut on every layer, so one snip gives matching holes.
- One fold and one punch give two holes; two folds give four; three folds give eight.
~30 min · full explanation, examples & memory tricks in the app
3
Rotational Symmetry
Some figures will not fold but still look unchanged when they are turned. The order counts the positions in a full turn, the smallest angle is 360 divided by the order, and order is never zero.
- A figure has rotational symmetry when turning it about a fixed point leaves it looking unchanged.
- The fixed point it turns about is called the centre of rotation.
- A turn that leaves the figure looking the same is an angle of symmetry, and 360 degrees always qualifies.
~35 min · full explanation, examples & memory tricks in the app
4
Radial Arms and Order
Arms drawn out of one point fit themselves only when the gaps between them are equal. Equal gaps share a full turn, so a figure of order n has a smallest angle of 360 divided by n.
- For a figure made of arms out of one point, the angles between neighbouring arms decide everything.
- A turn that fits the figure carries each gap onto the next, so all the gaps must be equal.
- Equal gaps share one full turn, so with n arms each gap measures 360 divided by n.
~35 min · full explanation, examples & memory tricks in the app
5
Circles, and Playing with Tiles
A circle turns onto itself at every angle and folds along every diameter, so it has no order at all. Colouring sectors or laying tiles lets you design the symmetry you want.
- A circle is turned onto itself by every angle there is, so it has no smallest angle and no order.
- Every diameter of a circle is a line of symmetry, and endlessly many diameters can be drawn.
- A circle is the one figure with unlimited amounts of both kinds of symmetry.
~30 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
145 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Rehana folds a paper leaf down its midrib and the two sides cover each other with nothing showing. What has she proved?
Beginner
A The midrib is a line of symmetry
B The leaf is a rectangle with equal sides
C The leaf has exactly four fold lines
D The midrib is the longest line she could draw
Show answer & explanation
The midrib is a line of symmetry
A fold that hides one half behind the other is the whole test.
A line that a figure can be folded along so the halves match is called a line of ____.
Beginner
A distance
B symmetry
C rotation
D measurement
Show answer & explanation
symmetry
That fold line is the line of symmetry, also called the axis of symmetry.
How many fold lines does a square have?
Beginner
A Two, and both of them run through opposite corners
B Three, one from every second corner
C Four, two through sides and two through corners
D Eight, one for each half of every side
Show answer & explanation
Four, two through sides and two through corners
The two side folds and the two diagonal folds make four in all.
Which statement about a rectangle 12 cm by 5 cm is true?
Intermediate
A Each of its two diagonals folds it into halves that match
B It has four fold lines, exactly like a square
C It cannot be folded into matching halves at all
D It has two fold lines, through the middles of opposite sides
Show answer & explanation
It has two fold lines, through the middles of opposite sides
Its diagonal folds fail, so only the two side folds are left.
🃏 Flashcards
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75 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
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Memory Match
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Fact Or Myth
Sequence Builder
True False
Fill Blank
Word Match
Speed Quiz
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