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Chapter 18 Symmetry Exercise 18.3

Question: 1

Give the order of rotational symmetry for each of the following figures when rotated about the marked point (x):



Solution:

(i) The given figure has its rotational symmetry as 4.

(ii) The given figure has its rotational symmetry as 3.

(iii) The given figure has its rotational symmetry as 3.

(iv) The given figure has its rotational symmetry as 4.

(v) The given figure has its rotational symmetry as 2.

(vi) The given figure has its rotational symmetry as 4.

(vii) The given figure has its rotational symmetry as 5.

(viii) The given figure has its rotational symmetry as 6.

(ix) The given figure has its rotational symmetry as 3.

 

Question: 2

Name any two figures that have both line symmetry and rotational symmetry.

Solution:

An equilateral triangle and a square have both lines of symmetry and rotational symmetry.



 

Question: 3

Give an example of a figure that has a line of symmetry but does not have rotational symmetry.

Solution:

A semicircle and an isosceles triangle have a line of symmetry but do not have rotational symmetry.



 

Question: 4

Give an example of a geometrical figure which has neither a line of symmetry nor a rotational symmetry.

Solution:

A scalene triangle has neither a line of symmetry nor a rotational symmetry.



 

Question: 5

Give an example of a letter of the English alphabet which has

(i) No line of symmetry

(ii) Rotational symmetry of order 2.

Solution:

(i) The letter of the English alphabet which has no line of symmetry is Z.

(ii) The letter of the English alphabet which has rotational symmetry of order 2 is N.

 

Question: 6

What is the line of symmetry of a semi-circle? Does it have rotational symmetry?

Solution:

A semicircle (half of a circle) has only one line of symmetry. In the figure, there is one line of symmetry. The figure is symmetric along the perpendicular bisector I of the diameter XY.

A semi-circle does not have any rotational symmetry.



 

Question: 7

Draw, whenever possible, a rough sketch of

(i) a triangle with both line and rotational symmetries.

(ii) a triangle with only line symmetry and no rotational symmetry.

(iii) a quadrilateral with a rotational symmetry but not a line of symmetry.

(iv) a quadrilateral with line symmetry but not a rotational symmetry.

Solution:

(i) An equilateral triangle has 3 lines of symmetry and a rotational symmetry of order 3.



(ii) An isosceles triangle has only 1 line of symmetry and no rotational symmetry.



(iii) A parallelogram is a quadrilateral which has no line of symmetry but a rotational symmetry of order 2.



(iv) A kite is a quadrilateral which has only one line of symmetry and no rotational symmetry.



 

Question: 8

Fill in the blanks:


	
		
	
	

		

			
Figures
			
Centre of rotation
			
Order of rotation
			
Angle of rotation  
		
		

			
Square
			
 
			
 
			
 
		
		

			
Rectangle
			
 
			
 
			
 
		
		

			
Rhombus
			
 
			
 
			
 
		
		

			
Equilateral triangle
			
 
			
 
			
 
		
		

			
Regular hexagon
			
 
			
 
			
 
		
		

			
Circle
			
 
			
 
			
 
		
		

			
Semi-circle
			
 
			
 
			
 
		
	


Solution:


	
		
	
	

		

			
Figures
			
Centre of rotation
			
Order of rotation
			
Angle of rotation  (°)
		
		

			

			
Square
			
			

			
Point of intersection of the line segments joining the mid-points of opposite sides.
			
			
4
			
90
		
		

			

			
Rectangle
			
			

			
Point of intersection of the line segments joining the mid-points of opposite sides
			
			
2
			
180
		
		

			

			
Rhombus
			
			

			
Point of intersection of diagonals
			
			
2
			
180
		
		

			

			
Equilateral triangle
			
			

			
Point of intersection of angle bisectors i.e, centroid
			
			
3
			
120
		
		

			

			
Regular hexagon
			
			

			
Centre of the hexagon
			
			
6
			
60
		
		

			

			
Circle
			
			

			
Centre of the circle
			
			
Unlimited
			
Any angle
		
		

			

			
Semi-circle
			
			

			
Nil
			
			
NIL
			
Nil
		
	


 

Question: 9

Fill in the blanks:


	
		
	
	

		

			
English alphabet Letter
			
Line Symmetry
			
Number of Lines of symmetry
			
Rotational Symmetry
			
Order of rotational Symmetry
		
		

			
Z
			
Nil
			
0
			
YES
			
2
		
		

			
S
			
–
			
–
			
–
			
–
		
		

			
H
			
YES
			
–
			
YES
			
–
		
		

			
O
			
YES
			
–
			
YES
			
–
		
		

			
E
			
YES
			
–
			
–
			
–
		
		

			
N
			
–
			
–
			
YES
			
–
		
		

			
C
			
–
			
–
			
–
			
–
		
	


Solution:


	
		
	
	

		

			
English alphabet Letter
			
Line Symmetry
			
Number of Lines of symmetry
			
Rotational Symmetry
			
Order of rotational Symmetry
		
		

			
Z
			
NO
			
0
			
YES
			
2
		
		

			
S
			
NO
			
0
			
YES
			
2
		
		

			
H
			
YES
			
2
			
YES
			
2
		
		

			
O
			
YES
			
4
			
YES
			
2
		
		

			
E
			
YES
			
1
			
NO
			
0
		
		

			
N
			
NO
			
0
			
YES
			
2
		
		

			
C
			
YES
			
1
			
NO
			
0
		
	

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