CBSE Class 6 Mathematics Symmetry MCQs Set 11

Answer: (b) A line along which the figure can be folded so that the two parts overlap exactly

Explanation:
1. A line of symmetry is a fold line: folding along it makes one part fall exactly on the other part.
2. A line can cut a figure into two parts of equal area and still fail this test (a diagonal of a rectangle does this), so (a) and (c) are not enough.
3. So the correct description is a line along which the folded parts overlap exactly.

Teacher's Note:
1. Equal area is not the same as exact overlap.
2. Always test a line of symmetry by folding.

Answer: (c) 4

Explanation:
1. A square sheet can be folded so that the halves overlap in four ways: the vertical fold, the horizontal fold and the two diagonal folds.
2. So a square has 4 lines of symmetry.

Teacher's Note:
1. Do not forget the two diagonals.
2. Try it with a square paper napkin.

Answer: (a) reflection symmetry

Explanation:
1. A line of symmetry acts like a mirror: each part on one side is the reflection of the part on the other side.
2. So such a figure is said to have reflection symmetry.

Teacher's Note:
1. Line symmetry and reflection symmetry mean the same thing.
2. Rotational symmetry is about turning, not folding.

Answer: (d) exactly 3 lines of symmetry

Explanation:
1. Such a triangle is an equilateral triangle.
2. The fold through each corner and the middle of the opposite side is a line of symmetry.
3. There are 3 corners, so there are exactly 3 lines of symmetry.

Teacher's Note:
1. One line of symmetry through each corner.
2. A regular polygon with n sides has n lines of symmetry.

Answer: (b) centre of rotation

Explanation:
1. In rotational symmetry the figure is turned about one fixed point.
2. That fixed point is called the centre of rotation.

Teacher's Note:
1. Think of the pin in the middle of a paper pinwheel.
2. The centre of rotation does not move.

Answer: (c) Both Statement I and Statement II are true

Explanation:
1. A full turn of 360° always brings any figure back to where it started, so Statement I is true.
2. All angles of symmetry are multiples of the smallest one, and 360° is one of them, so the smallest angle divides 360. Statement II is true.
3. So both statements are true.

Teacher's Note:
1. 360° works for every figure.
2. Smallest angle × order = 360°.

Answer: (d) Infinitely many

Explanation:
1. Every diameter of a circle is a line of symmetry.
2. A circle has endless diameters, so it has infinitely many lines of symmetry.

Teacher's Note:
1. Any fold through the centre works for a circle.
2. The circle is the most symmetric figure.

Answer: (a) A photograph of clouds in the sky

Explanation:
1. In a butterfly, a rangoli and the Taj Mahal, parts repeat in a definite pattern.
2. Clouds have puffs of all shapes and sizes with no repeating pattern.
3. So the photograph of clouds is not symmetrical.

Teacher's Note:
1. Symmetry needs a definite repeating pattern.
2. Natural shapes like clouds usually have none.

Answer: (a) Only Statement I is true

Explanation:
1. A triangle with three different sides (a scalene triangle) has no fold that makes the parts overlap, so Statement I is true.
2. That same triangle shows that Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. One example is enough to show a statement with 'every' is false.
2. Triangles have 3, 1 or 0 lines of symmetry.

Answer: (b) No, because the two parts do not fall on each other when the paper is folded along it

Explanation:
1. Fold a rectangular sheet along its diagonal: the two triangles are of the same size, but they do not sit exactly on each other; corners stick out.
2. So the diagonal is not a line of symmetry, because the parts do not overlap.
3. Option (d) is wrong because a line of symmetry can be horizontal or slanting too.

Teacher's Note:
1. Same size is not enough; the parts must overlap.
2. Try folding a postcard along its diagonal.

Answer: (a) 1

Explanation:
1. The letter E can be folded along the horizontal line through its middle arm: the top arm falls on the bottom arm.
2. No vertical fold works, because the arms all point to the right.
3. So E has exactly 1 line of symmetry.

Teacher's Note:
1. Check a horizontal fold and a vertical fold separately.
2. Letters like B, C, D and E have a horizontal line of symmetry.

Answer: (c) A is true, but R is false.

Explanation:
1. The fold along the vertical middle line and the fold along the horizontal middle line both work, so A is true.
2. A diagonal of such a rectangle is not a line of symmetry, so R is false.
3. So A is true but R is false.

Teacher's Note:
1. The two lines of a rectangle join the middles of opposite sides.
2. Diagonals work for a square, not for a longer rectangle.

Answer: (b) n

Explanation:
1. An equilateral triangle has 3 lines, a square 4, a regular pentagon 5, a regular hexagon 6.
2. So a regular polygon with n sides has n lines of symmetry.

Teacher's Note:
1. Check the rule on a triangle and a square.
2. Number of sides = number of lines for a regular polygon.

Answer: (c) 60°

Explanation:
1. Six equal arms share one full turn equally.
2. Angle between neighbouring arms = 360° ÷ 6 = 60°, the smallest turn that makes the design look the same.

Teacher's Note:
1. Smallest angle = 360° ÷ number of equal arms.
2. Each arm moves to the next arm's place.

Answer: (d) 8

Explanation:
1. Order of rotational symmetry = 360° ÷ smallest angle of symmetry.
2. 360° ÷ 45° = 8.

Teacher's Note:
1. Order × smallest angle = 360°.
2. Check: 8 × 45° = 360°.

Answer: (b) (i)-(r), (ii)-(s), (iii)-(q), (iv)-(p)

Explanation:
1. Rectangle (not a square): 2 lines, so (i)-(r). Equilateral triangle: 3 lines, so (ii)-(s).
2. Regular pentagon: 5 lines, so (iii)-(q). Isosceles triangle: 1 line, so (iv)-(p).
3. The match is (i)-(r), (ii)-(s), (iii)-(q), (iv)-(p).

Teacher's Note:
1. Fix the easiest pair first.
2. Regular polygon: lines = sides.

Answer: (b) Only Statement II is true

Explanation:
1. A paper windmill turns onto itself, but no fold makes its halves overlap, so Statement I is false.
2. The windmill looks the same after turns of 90°, 180°, 270° and 360°, which are 4 angles of symmetry, and it has no line of symmetry. Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. Rotational symmetry can exist without line symmetry.
2. The windmill is the standard example.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Every figure comes back to itself after a full turn, so 360° alone tells us nothing special.
2. Rotational symmetry needs a matching turn of less than a full turn; this is what R says, so R is true.
3. Because of R, a figure with only 360° has no rotational symmetry, so A is true and R explains it.

Teacher's Note:
1. 360° does not count as rotational symmetry.
2. Look for a turn smaller than a full turn.

Answer: (c) 4

Explanation:
1. The plus-shaped tile can be folded along the vertical line and the horizontal line through its centre.
2. It can also be folded along the two slanting lines through its centre, as each arm falls on a neighbouring arm.
3. So it has 4 lines of symmetry.

Teacher's Note:
1. The plus tile is made of five equal squares, so it behaves like a square.
2. Check the slanting folds too.

Answer: (d) (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q)

Explanation:
1. A square comes onto itself after 90°, 180°, 270° and 360°, so its order is 4: (i)-(r).
2. A rectangle has order 2: (ii)-(p). An equilateral triangle has order 3: (iii)-(s). A regular hexagon has order 6: (iv)-(q).
3. The match is (i)-(r), (ii)-(p), (iii)-(s), (iv)-(q).

Teacher's Note:
1. For a regular polygon, order = number of sides.
2. A rectangle only works with a half turn.

Answer: (a) a triangle with exactly two equal sides

Explanation:
1. Reflect the right-angled half in the dashed line to get a matching half on the left.
2. The two slanting sides of the full figure are reflections of each other, so they are equal.
3. The base is twice the short side of the half; it is a little shorter than each slanting side, so it is not equal to them.
4. So the completed figure is a triangle with exactly two equal sides.

Teacher's Note:
1. A side and its mirror image are always equal.
2. Joining two right-angled halves along a leg gives an isosceles triangle.

Answer: (c) 210°

Explanation:
1. The angles of symmetry are the multiples of 60°: 60°, 120°, 180°, 240°, 300°, 360°.
2. 210 ÷ 60 = 3.5 is not a whole number, so 210° is not an angle of symmetry.

Teacher's Note:
1. List the multiples of the smallest angle up to 360°.
2. Check each option by division.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The Chakra has 24 equally spaced spokes, so it looks the same after every 15° turn, giving 24 angles of symmetry. A is true.
2. Every diameter of a circle is indeed a line of symmetry, so R is true.
3. R talks about lines of a plain circle, not about the turns of the Chakra, so R does not explain A.

Teacher's Note:
1. Check whether R is about the same idea as A.
2. 24 spokes give 24 angles: 15°, 30°, …, 360°.

Answer: (d) Neither Statement I nor Statement II is true

Explanation:
1. A rectangle that is not a square has only 2 lines of symmetry, so Statement I is false.
2. A parallelogram that is not a rectangle (and not a rhombus) has no line of symmetry; it only looks the same after a half turn. Statement II is false.
3. So neither statement is true.

Teacher's Note:
1. Only the square among these has 4 lines.
2. A parallelogram has rotational symmetry but no line symmetry.

Answer: (c) A is true, but R is false.

Explanation:
1. A triangle has 3, 1 or 0 lines of symmetry; never exactly 2. So A is true.
2. A triangle with all three sides different has no line of symmetry, so R is false.
3. So A is true but R is false.

Teacher's Note:
1. Two lines in a triangle would force all three sides to be equal, giving 3 lines.
2. A scalene triangle disproves R.

Answer: (c) 20°

Explanation:
1. All angles of symmetry are multiples of the smallest one, and 60° must be one of them.
2. If the smallest angle is 20°, the angles below 60° are 20° and 40° only: exactly two. And 60° = 3 × 20°.
3. (10° would give five angles below 60°, 15° three, 30° only one.) So the answer is 20°.

Teacher's Note:
1. Count the multiples below 60° for each option.
2. 60 ÷ smallest angle − 1 = number of angles below 60°.

Answer: (d) A is false, but R is true.

Explanation:
1. The smallest angle of symmetry must divide 360° exactly.
2. 360 ÷ 17 is not a whole number, so 17 is not a factor of 360: R is true.
3. So no such figure can be drawn, and A is false.

Teacher's Note:
1. The smallest angle (in whole degrees) must be a factor of 360.
2. Here A is false even though R is true.

Answer: (d) 5

Explanation:
1. Count the arms: the same curved arm appears 5 times around the centre.
2. The design matches itself after turns of 72°, 144°, 216°, 288° and 360°.
3. So its order of rotational symmetry is 5.

Teacher's Note:
1. Order = number of identical repeated arms.
2. Smallest angle here is 360° ÷ 5 = 72°.

Answer: (a) (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q)

Explanation:
1. Equilateral triangle: 3 lines and 3 angles, (i)-(r). Rectangle (not a square): 2 lines and 2 angles, (ii)-(s).
2. Paper windmill: no line but 4 angles, (iii)-(p). Circle: infinitely many lines and every angle, (iv)-(q).
3. The match is (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. Match the windmill and the circle first; they are the special ones.
2. Then the counts 3 and 2 fit easily.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. With 12 equal repeats the order of rotational symmetry is 12.
2. By R, smallest angle = 360° ÷ 12 = 30°, so A is true.
3. R is true and is exactly the rule used to get A, so R explains A.

Teacher's Note:
1. Order × smallest angle = 360°.
2. 12 × 30° = 360° checks it.