Class 6 - Mathematics
Chapter - Symmetry : Exercise 14.3
Top Block 1
Question: 1. Name any two figures that have both line symmetry and rotational symmetry.
Answer :
Circle and Square.
Question: 2. Draw, wherever possible, a rough sketch of:
a triangle with both line and rotational symmetries of order more than 1.
a triangle with only line symmetry and no rotational symmetry of order more than 1.
a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Answer :
(i) An equilateral triangle has both line and rotational symmetries of order more than 1.
Rotational symmetry:
Mddle block 1
(iii)It is not possible because order of rotational symmetry is more than 1 of a figure, most acertain the line of symmetry.
(iv)A trapezium which has equal non-parallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than
1.
Rotational symmetry:
Question: 3. In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Answer :
Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.
Question: 4. Fill in the blanks:
| Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
|---|---|---|---|
| Square | |||
| Rectangle | |||
| Rhombus | |||
| Equilateral triangle | |||
| Regular hexagon | |||
| Circle | |||
| Semi-circle |
Answer :
Sol.
| Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
|---|---|---|---|
| Square | Intersecting point of diagonals. | 4 | 90o |
| Rectangle | Intersecting point of diagonals. | 2 | 180o |
| Rhombus | Intersecting point of diagonals. | 2 | 180o |
| Equilateral triangle | Intersecting point of medians. | 3 | 120o |
| Regular hexagon | Intersecting point of diagonals. | 6 | 60o |
| Circle | Centre | Infinite | At every point |
| Semi-circle | Mid-point of diameter | 1 | 360o |
Question: 5. Name the quadrilateral which has both line and rotational symmetry of order more than 1.
Answer :
Square has both line and rotational symmetry of order more than 1.
Line symmetry:
Question: 6. After rotating by 60o about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Answer :
Other angles will be 120o,180o,240o,300o,360o.
For rotation:It will rotate six times.
Question: 7. Can we have a rotational symmetry of order more than 1 whose angle of rotation is: (i) 45o(ii) 17o ?
Answer :
(i) If the angle of rotation is 45o, then symmetry of order is possible and would be 8 rotations.
(ii) If the angle of rotational is 17o, then symmetry of order is not possible because 360o is not complete divided by 17o.