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Class 6 Maths: Symmetry, 8 practice questions with answers

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These are 8 practice questions on Chapter 9, Symmetry, of the new NCERT Class 6 Maths textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover counting lines of symmetry, where points go in a reflection, symmetry in letters, the angles of symmetry of a wheel with spokes and bolts, which smallest angles of symmetry are possible, a two-coloured star, a figure with a half turn but no mirror line, and why two crossing mirror lines give a half turn. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was checked by a test script. Each question has its own setting and none retells a figure, worked example or exercise from the chapter, though common shapes such as the rectangle appear in both. No practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 6, Chapter 9, printed pages 217 to 241):

Lines of symmetry and reflection

Question 1. How many lines of symmetry does each shape have? (a) A kite: two short equal sides at the top and two long equal sides at the bottom. (b) A semicircle. (c) A window shaped like a rectangle with a semicircle on top. (d) The outline of a running track: two equal straight sides joined at the ends by two equal semicircles. (e) Three equal squares joined in a row.

Answer: (a) 1; (b) 1; (c) 1; (d) 2; (e) 2. (a) A kite folds onto itself only along the line through its top and bottom corners, where the equal sides meet: 1. (b) A semicircle folds only along the line from the middle of its straight edge through the top of the curve: 1. (c) The window folds only along its upright middle line; a sideways fold would put the curved top onto the flat bottom: 1. (d) The track folds along the line through the middles of its two straight sides, and along the line through the middles of its two curved ends: 2. (e) The row of squares folds along the line across the middle of the row's length (through the middle square) and along the line through the middle of its height: 2. Its diagonals are not lines of symmetry. (Lines of symmetry, pages 219 to 221.)

Question 2. On squared paper, a mirror line is drawn up the page, 5 squares from the left edge. A small flag has three corners: the foot of its pole is 2 squares from the left edge and 3 squares up, written (2, 3); the top of the pole is at (2, 7); and the tip of the flag is at (4, 6). (a) Where do the three corners go when the flag is reflected in the mirror line? (b) Which corner of the flag is nearest the mirror line, and how far is its reflection from the line? (c) A dot at (5, 4) is also reflected. Where does it go?

Answer: (a) (8, 3), (8, 7) and (6, 6); (b) the tip, 1 square from the line, and its reflection is also 1 square away; (c) it stays at (5, 4). (a) A reflection keeps each point at the same height and puts it the same distance from the mirror line, on the other side. The foot is 3 squares left of the line, so it goes to 3 squares right of it: 5 + 3 = 8, so (8, 3). In the same way the top of the pole goes to (8, 7) and the tip, 1 square left of the line, goes to (6, 6). (b) The tip is nearest, 1 square from the line, and its reflection is also 1 square from it, on the other side. (c) A point on the mirror line is its own reflection, so the dot does not move. (Reflection, pages 221 and 222.)

Question 3. Written as plain capital letters, how many lines of symmetry do H, N, E, A and S have? Which of them look the same after a half turn?

Answer: H has 2, E has 1, A has 1, and N and S have none; H, N and S look the same after a half turn. H folds along a vertical line and a horizontal line: 2. E folds only along a horizontal line: 1. A folds only along a vertical line: 1. N and S do not fold onto themselves along any line: 0. But turning H, N or S through 180° gives the same letter, so H, N and S have rotational symmetry; E and A do not. (Lines of symmetry and angles of symmetry, pages 219 and 230 to 232.)

Angles of symmetry

Question 4. A cycle wheel has 6 spokes, evenly spaced, and 4 shiny bolts, also evenly spaced, around the same centre. (a) What is the smallest turn that makes the whole wheel, spokes and bolts together, look the same? (b) List all its angles of symmetry. (c) What would the smallest turn be with 8 spokes and 12 bolts?

Answer: (a) 180°; (b) 180° and 360°; (c) 90°. (a) The spokes alone look the same after turns of 60°, 120°, 180°, … (multiples of 360° ÷ 6). The bolts alone look the same after 90°, 180°, 270°, … (multiples of 360° ÷ 4). The whole wheel looks the same only after a turn that is in both lists, and the smallest is 180°. (b) Turns of 180° and 360°. (c) The spokes need a multiple of 360° ÷ 8 = 45° and the bolts a multiple of 360° ÷ 12 = 30°. The smallest turn in both lists is 90°, and the angles of symmetry are 90°, 180°, 270° and 360°. (Radial arms and angles of symmetry, pages 232 to 236.)

Question 5. (a) List every whole number of degrees from 10° to 30° that can be a figure's smallest angle of symmetry, and the number of equal radial arms that would give each one. (b) Which of these figures also have 90° as an angle of symmetry?

Answer: (a) 10° (36 arms), 12° (30), 15° (24), 18° (20), 20° (18), 24° (15) and 30° (12); (b) the ones with 10°, 15°, 18° and 30°. (a) A whole-number smallest angle of symmetry must divide 360 exactly. Testing 10 to 30, the numbers that divide 360 are 10, 12, 15, 18, 20, 24 and 30. A figure of equal arms with gaps of that angle needs 360 ÷ angle arms: 36, 30, 24, 20, 18, 15 and 12. The rest leave a remainder; for example, 360 ÷ 16 = 22 with 8 left over. (b) Every angle of symmetry is a multiple of the smallest one, so 90° is an angle of symmetry only when the smallest angle divides 90 exactly: 90 ÷ 10 = 9, 90 ÷ 15 = 6, 90 ÷ 18 = 5 and 90 ÷ 30 = 3, but 12, 20 and 24 do not divide 90. So 10°, 15°, 18° and 30°. (Multiples of the smallest angle, and why it divides 360, pages 236 and 237.)

Question 6. A six-pointed star is made of a red equilateral triangle and a blue equilateral triangle of the same size, one pointing up and one pointing down, with the same centre. The colours count: a line or a turn works only if red lands on red and blue on blue. (a) How many lines of symmetry does the star have? (b) What are its angles of symmetry? (c) What would the answers be if both triangles were red?

Answer: (a) 3; (b) 120°, 240° and 360°; (c) 6 lines and 6 angles of symmetry. (a) A line through the tip of a red point passes through the centre and on to the tip of the blue point opposite it. Folding along it keeps the red triangle on itself and the blue triangle on itself, so it works; there are 3 such lines. The other 3 lines, through the dents between the points, swap red with blue, so they do not work: 3 lines. (b) A turn of 60° moves the red points onto the blue ones, so it fails; a turn of 120° moves each red point onto the next red point and each blue onto blue: 120°, 240° and 360°. (c) With one colour, the colour no longer stops anything: 6 lines, and every multiple of 60° up to 360° becomes an angle of symmetry: 6 angles. (Lines and angles of symmetry, pages 219 to 221 and 230 to 236.)

Both kinds of symmetry

Question 7. A rectangle made of 6 squares, 2 rows of 3, has its top-left square and its bottom-right square shaded. (a) Does it have a line of symmetry? (b) What are its angles of symmetry? (c) Which two squares could you shade instead so that it has 2 lines of symmetry?

Answer: (a) no; (b) 180° and 360°; (c) the top-middle and bottom-middle squares. (a) The only fold lines of the plain rectangle are its upright middle line and its sideways middle line. The upright one sends the shaded top-left square onto the unshaded top-right square, and the sideways one sends it onto the unshaded bottom-left square, so neither works. (b) A half turn about the centre sends the top-left square to the bottom-right square and the bottom-right to the top-left, so the shading lands on shading: 180° and 360° are angles of symmetry. This is a figure with rotational symmetry but no reflection symmetry. (c) Shade the top-middle and bottom-middle squares: the upright fold keeps each of them in place, and the sideways fold swaps them, so both middle lines work, and the half turn still works too. (Figures with one kind of symmetry and not the other, pages 230 to 231 and 238.)

Question 8. Raju says: "If a figure has two lines of symmetry that cross at right angles, it will also look the same after a half turn about the point where they cross." (a) Test this on a rectangle that is not a square, the letter H and the letter O. (b) Is Raju right? Explain why, by following one point through both folds.

Answer: (a) all three look the same after a half turn; (b) yes. (a) A rectangle has an upright and a sideways line of symmetry and looks the same after 180°. H has the same two lines and looks the same upside down. A plain O also has both lines and the same half turn. (b) Mark a point in the top-right part of the figure. Folding along the upright line sends it to the same height on the left; folding along the sideways line then sends it to the same distance below the middle. It has ended up in the bottom-left part, exactly opposite where it started, across the centre, which is where a half turn would take it. Both folds keep the figure the same, so the half turn does too: Raju is right. (Reflection symmetry and rotational symmetry, pages 221 and 230 to 231.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 216 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every answer was checked by script. This guide is general information; follow your teacher and the textbook.