Exercise 14.3
Question 1:
Name any two figures that have both line symmetry and rotational symmetry.
Answer 1:
Circle and Square.
Question 2:
Draw, wherever possible, a rough sketch of:
(i) a triangle with both line and rotational symmetries of order more than 1.
(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.
(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Answer 2:
(i) An equilateral triangle has both line and rotational symmetries of order more than 1.
Line symmetry:
Rotational symmetry:
(ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.
Line symmetry:
Rotational symmetry:
(iii) A quadrilateral with no line of symmetry is an irregular quadrilateral
Checking rotational symmetry
If it is rotated 90°
It does not looks same as initial figure
If it is rotated 180°
It does not looks same as initial figure
If it is rotated 360°
It looks same as initial figure
Thus,
Thus, order of rotational symmetry - 1
Hence,
A quadrilateral with a rotational symmetry of order not a line of symmetry Is not possible
(iv) A trapezium which has equal non-parallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Line symmetry:
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 3:
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 |
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| |
Rectangle |
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| |
Rhombus |
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| |
Equilateral triangle |
|
| |
Regular hexagon |
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| |
Circle |
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| |
Semi-circle |
Answer 4:
Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
Square | Intersecting point of diagonals. | 4 | 90° |
Rectangle | Intersecting point of diagonals. | 2 | 180° |
Rhombus | Intersecting point of diagonals. | 2 | 180° |
Equilateral triangle | Intersecting point of medians. | 3 | 120° |
Regular hexagon | Intersecting point of diagonals. | 6 | 60° |
Circle | Centre | infinite | At every point |
Semi-circle | Mid-point of diameter | 1 | 360° |
Question 5:
Name the quadrilateral which has both line and rotational symmetry of order more than 1.
Answer 5:
Square has both line and rotational symmetry of order more than 1.
Line symmetry:
Rotational 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 6:
Other angles will be 120°, 180°,240°,300°,360°.
For 60° rotation:
It will rotate six times.
For 120° rotation:
It will rotate three times.
For 180° rotation:
It will rotate two times.
For 360° rotation:
It will rotate one time.
Question 7:
Can we have a rotational symmetry of order more than 1 whose angle of rotation is:
(i) 45o
(ii) 17o ?
Answer 7:
(i) If tiie angle of rotation is 45°, then symmetry of order is possible and would be 8 rotations.
(ii) If the angle of rotational is 17°, then symmetry o f order is not possible because 360° is not complete divided by 17°.
1. What is symmetry? |
2. How is symmetry useful in daily life? |
3. What are the different types of symmetry? |
4. How can symmetry be identified in geometric shapes? |
5. Can all objects have symmetry? |
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