E ExamMaster

CBSE Class 6 · Mathematics

Symmetry

Official NCERT chapter from Ganita Prakash (book code fegp1). ExamMaster notes are original teaching at CBSE Class 6 depth.

This lesson follows the official chapter “Symmetry” in Ganita Prakash. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 6
  • Easy level
  • 8 concepts

1Line of Symmetry

A line of symmetry is a fold (or reflection) that lands the figure on itself. A dashed line is a candidate until it lands.

Drawing the line does not earn the title.

Figure. A line of symmetry is a fold test: the two sides must land on each other. This isosceles triangle passes the vertical fold — matching base corners, matching slanted sides. A line you can draw that does not pass the landing test is only a decoration.

How it works

  1. Draw a candidateA dashed line.
  2. Fold or match halvesThe test.
  3. Title it only if it landsThen it is a line of symmetry.

2Rotational Symmetry

A figure has rotational symmetry if a turn about a centre, less than a full turn, lands on itself. Order is how many such landings in a full turn (including the full turn).

A fold-pass is not automatically a turn-pass.

Figure. Rotational symmetry is a turn test: some angle less than a full turn lands on the same drawing. This plus looks the same after 90°, so its order is 4. A half-turn (180°) is the other common school test — still a landing, not a spin for its own sake.

How it works

  1. Pick a centreA point.
  2. Turn until it first landsA fraction of a full turn.
  3. Count landings in one full turnThe order.

3Figures with more than one line of symmetry

A square can have four lines; an equilateral triangle three; a non-square rectangle two. Each line is its own test.

One pass does not gift the next line.

Figure. A square passes four fold tests: two mid-lines and two diagonals. A non-square rectangle keeps only the mid-lines — the diagonals fail. Count the lines that land, do not count every line you can draw.

How it works

  1. Run fold 1Pass or fail.
  2. Run the next candidateA new test.
  3. Count only the lines that landedTwo or more if they all pass.

4A fold is a test, not a decoration

Ink, a dashed style, or a pretty crease is decoration. Landing is the test.

A decorated fail is still a fail.

Figure. A fold is a test, not a decoration. The left triangle is cut by a line that really matches both sides. The right triangle has a neat dashed line that does not make the unmatched peak land — so that line is not a line of symmetry.

How it works

  1. FoldSee the miss or the land.
  2. Ignore how pretty the crease looksDecoration.
  3. Name pass or failThe test.

5A turn can be a symmetry test too

A half-turn of a parallelogram (that is not a rectangle) can land when a fold fails. Name which test you ran.

Do not swap the words fold and turn.

Figure. A turn can be a symmetry test too. Mark a corner A on a rectangle, rotate 180° about the centre, and A lands on the opposite corner — the drawing is the same. A 90° turn would not land, so this rectangle’s rotational order is 2, not 4.

How it works

  1. Name the testFold, or turn.
  2. Run only that testEvidence.
  3. Report that test’s resultDo not gift the other.

6A rectangle that is not a square fails the diagonal fold

Vertical and horizontal midlines can pass. The diagonal of a long rectangle does not land: sides do not match.

Do not copy a square’s four lines onto a long rectangle.

Figure. A rectangle that is not a square fails the diagonal fold: the short side cannot cover the long side, so the corners do not land. Mid-line folds still pass. The diagonal is the test that separates rectangle from square.

How it works

  1. Try the two midlinesOften pass.
  2. Try a diagonalFail if it is not a square.
  3. Count two lines, not fourHonest for a non-square rectangle.

Rectangle diagonals

A 2-by-6 rectangle: do the two midlines pass? Does a diagonal?

  • Midlinespass (two lines)
  • Diagonalfail — not a square
  • Lines of symmetry2, not 4

Pro tip. A square’s extra lines are not a gift to every rectangle.

7An ink blot is evidence of a fold

Paint on one side, fold, press: the blot is a record of that fold. If the two sides match, that fold was a line of symmetry of the blot.

A blot you painted on both sides freely is not evidence of one fold.

Figure. An ink blot is evidence of a fold: paint on one half, close the fold, and a matching blot appears as the partner. The pair is the proof that that line was a line of symmetry — the blot did the landing test for you.

How it works

  1. Fold first or press after paint on one sideThe method.
  2. Open and see the matchEvidence.
  3. Name that crease as the candidate that landedFor this blot.

8Almost even fails the test

A petal that misses its partner by a little still fails. Almost is a miss.

Do not “give it” because it looks nearly even.

Figure. Almost even fails the test. The two eyes sit on different heights, so the hoped-for midline does not make them land. Near-symmetry is still a fail — the fold does not get a consolation mark.

How it works

  1. See the missA part sticks out.
  2. Call fail for that line or turnExact landing.
  3. Try another candidate if the task allowsA new test.
A non-square rectangle’s diagonal fold
  1. Fails — do not copy a square’s four lines
  2. Always passes
  3. Is a turn-test

Two midlines, not the diagonals.

Notes

  • The official chapter title is “Symmetry”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Recap

Hold these pegs from the official chapter “Symmetry”. The wording is ExamMaster’s teaching, not a textbook recap.

Line of Symmetry
A line of symmetry is a fold (or reflection) that lands the figure on itself.
Rotational Symmetry
A figure has rotational symmetry if a turn about a centre, less than a full turn, lands on itself.
Figures with more than one line of symmetry
A square can have four lines; an equilateral triangle three; a non-square rectangle two.
A fold is a test, not a decoration
Ink, a dashed style, or a pretty crease is decoration.
A turn can be a symmetry test too
A half-turn of a parallelogram (that is not a rectangle) can land when a fold fails.
A rectangle that is not a square fails the diagonal fold
Vertical and horizontal midlines can pass.

Practise Symmetry

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
Continue with Google — freeNo card, no trial. Works offline once installed.