CBSE Class 6 Mathematics Symmetry Assignment Set 02

Very Short Answer Questions

Question 1. What do we mean when we say that a figure is symmetrical?
Answer:
A figure is symmetrical when a part or parts of it repeat in a definite pattern, like the two wings of a butterfly or the petals of a rangoli.

Teacher's Note:
1. Look for parts that repeat in a fixed way.
2. Folding or turning can show the repeat.

Question 2. Define a line of symmetry of a plane figure.
Answer:
A line of symmetry (axis of symmetry) is a line that divides a figure into two parts which overlap exactly when the figure is folded along that line.

Teacher's Note:
1. The key words are 'fold' and 'overlap exactly'.
2. Equal size alone is not enough.

Question 3. From this list - butterfly, rangoli, clouds, flower - name the one that is not symmetrical.
Answer:
The clouds are not symmetrical, because no part of them repeats in a definite pattern.

Teacher's Note:
1. Natural shapes like clouds have no regular pattern.
2. The others all have repeating parts.

Question 4. How many lines of symmetry does the picture of a butterfly with open wings have?
Answer:
It has 1 line of symmetry: the vertical line along the body, between the two wings.

Teacher's Note:
1. The left wing is the mirror image of the right wing.
2. No other fold works.

Question 5. Name the line of symmetry that you can see in the front view of the Taj Mahal.
Answer:
The vertical line through the centre of the building, passing through the main dome; the left and right halves are mirror images.

Teacher's Note:
1. Famous buildings are often designed to be symmetrical.
2. The line passes through the main dome.

Question 6. How many lines of symmetry does a square have?
Answer:
A square has 4 lines of symmetry.

Teacher's Note:
1. Two middle lines and two diagonals.
2. Fold a square paper to check.

Question 7. Name the four folds of a square sheet of paper that give its lines of symmetry.
Answer:
The vertical fold, the horizontal fold and the two diagonal folds.

Teacher's Note:
1. The middle folds join middles of opposite sides.
2. Diagonal folds join opposite corners.

Question 8. How many lines of symmetry does a triangle with equal sides and equal angles have?
Answer:
This is an equilateral triangle; it has 3 lines of symmetry.

Teacher's Note:
1. One line through each corner.
2. Each line meets the middle of the opposite side.

Question 9. Does a triangle whose three sides are of different lengths have any line of symmetry?
Answer:
No. A triangle with all three sides different has no line of symmetry.

Teacher's Note:
1. No fold makes its parts overlap.
2. Such a triangle is called scalene.

Question 10. What kind of symmetry is a figure said to have when it has one or more lines of symmetry?
Answer:
It has reflection symmetry, because each half is the mirror reflection of the other half in that line.

Teacher's Note:
1. Line symmetry is also called reflection symmetry.
2. The line acts like a mirror.

Question 11. What is the centre of rotation of a figure?
Answer:
It is the fixed point about which the figure is turned when we check it for rotational symmetry.

Teacher's Note:
1. The centre of rotation does not move during the turn.
2. For a fan it is the middle of the hub.

Question 12. Which angle is an angle of symmetry of every figure? Why?
Answer:
360°. After one full turn, every figure comes back exactly to its starting position.

Teacher's Note:
1. A full turn always works.
2. So 360° alone does not mean rotational symmetry.

Question 13. How many lines of symmetry does a rectangle that is not a square have? Name them.
Answer:
It has 2 lines of symmetry: the vertical line and the horizontal line through its centre (each joining the middles of opposite sides).

Teacher's Note:
1. Its diagonals are not lines of symmetry.
2. Fold a postcard to check.

Question 14. Is a diagonal of a rectangle that is not a square a line of symmetry? Give a reason.
Answer:
No. Folding along a diagonal gives two triangles of the same size, but they do not fall exactly on each other.

Teacher's Note:
1. Same size does not mean they overlap.
2. Diagonals work only when the rectangle is a square.

Question 15. Ink is dropped on one half of a folded sheet, the halves are pressed together and the sheet is opened. Where is the line of symmetry of the blot formed?
Answer:
The line of symmetry is the fold line of the paper, because the ink prints the same shape on both sides of the fold.

Teacher's Note:
1. The fold always becomes the mirror line.
2. This is the ink blot activity.

Question 16. A single hole is punched in a folded square sheet. On opening the sheet, two holes are seen. Where does the fold line lie?
Answer:
The fold line lies exactly midway between the two holes; it is the line of symmetry of the pair of holes.

Teacher's Note:
1. Both holes are at equal distances from the fold.
2. The fold is the mirror line.

Question 17. Half of a figure is drawn on one side of a given line. How will you complete the figure so that the given line is its line of symmetry?
Answer:
Reflect each corner in the line: mark a point at the same distance on the other side of the line, at the same level, and join the marked points in the same order.

Teacher's Note:
1. Count squares or dots to keep distances equal.
2. Points on the line stay where they are.

Question 18. A square ABCD is reflected in its vertical line of symmetry. Which corner takes the place of A?
Answer:
If A and B are the two top corners, then B takes the place of A (and A takes the place of B; C and D also swap).

Teacher's Note:
1. A vertical mirror line swaps left and right.
2. Corners at the same height exchange places.

Question 19. How many lines of symmetry does a regular polygon with 9 equal sides have?
Answer:
It has 9 lines of symmetry, since a regular polygon with n sides has n lines of symmetry.

Teacher's Note:
1. Lines = sides for a regular polygon.
2. This 9-sided polygon is a nonagon.

Question 20. What is meant by the order of rotational symmetry of a figure?
Answer:
It is the number of times the figure looks exactly the same during one full turn about its centre, that is, the number of its angles of symmetry.

Teacher's Note:
1. Count the matching positions in one full turn.
2. Order × smallest angle = 360°.

Question 21. Write all the angles of symmetry of a square.
Answer:
90°, 180°, 270° and 360°.

Teacher's Note:
1. They are multiples of 90°.
2. So a square has order 4.

Question 22. Give two examples of objects around you that have rotational symmetry.
Answer:
A bicycle wheel and a ceiling fan (a flower and a rangoli are other examples).

Teacher's Note:
1. Look for objects with identical repeated parts around a centre.
2. Things that spin are good examples.

Question 23. A design has 5 radial arms placed at equal angles about its centre. What is its smallest angle of symmetry?
Answer:
Smallest angle of symmetry = 360° ÷ 5 = 72°.

Teacher's Note:
1. Divide 360° by the number of equal arms.
2. Check: 5 × 72° = 360°.

Question 24. How many lines of symmetry does a circle have, and what are these lines called?
Answer:
A circle has infinitely many lines of symmetry; each one is a diameter of the circle.

Teacher's Note:
1. Every fold through the centre works.
2. There are endless diameters.

Question 25. The angles of symmetry of a figure are multiples of which angle? Write the angles of symmetry of a figure whose smallest angle of symmetry is 120°.
Answer:
They are multiples of the smallest angle of symmetry. Here they are 120°, 240° and 360°.

Teacher's Note:
1. Keep adding the smallest angle until you reach 360°.
2. This figure has order 3.

Question 26. A design has 7 radial arms placed at equal angles about its centre. Write its smallest angle of symmetry as a mixed fraction.
Answer:
Smallest angle = 360° ÷ 7 = \( 51\frac{3}{7} \)° (since 7 × 51 = 357 and 3 is left over), which is not a whole number of degrees.

Teacher's Note:
1. Divide and write the remainder over 7.
2. Not every angle of symmetry is a whole number.

Question 27. Can a figure have 50° as its smallest angle of symmetry? Give a reason.
Answer:
No. The smallest angle of symmetry must divide 360° exactly, but 360 ÷ 50 = 7.2 is not a whole number.

Teacher's Note:
1. Test by dividing 360 by the angle.
2. Factors of 360 like 40, 45, 60 would work.

Question 28. The smallest angle of symmetry of a wheel design is 40°. Find its order of rotational symmetry.
Answer:
Order = 360° ÷ 40° = 9, so the design looks the same 9 times in one full turn.

Teacher's Note:
1. Order = 360° ÷ smallest angle.
2. Check: 9 × 40° = 360°.

Question 29. Name a quadrilateral that has rotational symmetry but no line of symmetry.
Answer:
A parallelogram that is not a rectangle or a rhombus; it looks the same after a half turn of 180° but has no line of symmetry.

Teacher's Note:
1. Its angles of symmetry are 180° and 360°.
2. No fold makes its halves overlap.

Question 30. How many lines of symmetry and how many angles of symmetry does the Ashoka Chakra have?
Answer:
It has 24 lines of symmetry and 24 angles of symmetry, because its 24 spokes are equally spaced.

Teacher's Note:
1. Smallest angle = 360° ÷ 24 = 15°.
2. Lines pass through spokes and through gaps.