Chapter 14 Symmetry Exercise 14.3
Question 1: Name any two figures that have both line symmetry and rotational symmetry.
Answer: Equilateral triangle and Circle are the 2 figures that have both line symmetry and rotational symmetry.
Question 2: Draw, wherever possible, a rough sketch of
(i) A triangle with both line and rotational symmetries of order more than 1.
Answer:
Line symmetry
Rotational symmetry
(ii) A triangle with only line symmetry and no rotational symmetry of order more than 1.
Answer:
(iii) A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
Answer: A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry cannot be drawn as a quadrilateral with a line symmetry may have rotational symmetry of order one but not more than one.
(iv) A quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Answer:
Question 3: If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Answer: Yes, if a figure has two or more lines of symmetry, then it will have rotational symmetry of order more than 1.
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:
Shape |
Centre of Rotation |
Order of Rotation |
Angle of Rotation |
Square |
Intersecting point of diagonals |
4 |
90^{o} |
Rectangle |
Intersecting point of diagonals |
2 |
180^{o} |
Rhombus |
Intersecting point of diagonals |
2 |
180^{o} |
Equilateral Triangle |
Intersecting point of medians |
3 |
120^{o} |
Regular Hexagon |
Intersecting point of diagonals |
6 |
60^{o} |
Circle |
Centre |
Infinite |
Every angle |
Semi-circle |
Mid-point of diameter |
1 |
360^{o} |
Question 5: Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer: The quadrilateral which have both line and rotational symmetry of order more than 1 is a square.
Line symmetry:
Rotational symmetry:
Question 6: After rotating by 60° about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Answer: The other angles are 120°, 180°, 240°, 300°, and 360°.
Question 7: Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°?
Answer: Yes, it is possible to have a rotational symmetry of order more than 1 whose angle of rotation is 45°.
(ii) 17°?
Answer: No, it is not possible to have a rotational symmetry of order more than 1 whose angle of rotation is 17°.
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