RD Sharma 2017 Solutions for Class 7 Math Chapter 18 Symmetry are provided here with simple step-by-step explanations. These solutions for Symmetry are extremely popular among class 7 students for Math Symmetry Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma 2017 Book of class 7 Math Chapter 18 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma 2017 Solutions. All RD Sharma 2017 Solutions for class 7 Math are prepared by experts and are 100% accurate.

Page No 18.16:

Question 1:

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

Answer:

(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.

Page No 18.16:

Question 2:

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

Answer:

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

Page No 18.16:

Question 3:

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

Answer:

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

Page No 18.16:

Question 4:

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

Answer:

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

Page No 18.16:

Question 5:

Give an example of a letter of the English alphabet which has (i) no line of symmetry and (ii) rotational symmetry of order 2.

Answer:

(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.

Page No 18.16:

Question 6:

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

Answer:

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 l of the diameter XY.


A semi-circle does not have any rotational symmetry.

Page No 18.16:

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.

Answer:

(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.
    

Page No 18.16:

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      

Answer:



Page No 18.17:

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

Answer:

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 Infinite Yes Infinite
E Yes 1 No 0
N No 0 Yes 2
C Yes 1 No 0

Page No 18.17:

Question 1:

Which of the following has only 2 lines of symmetry?
(a) Equilateral triangle
(b) Rhombus
(c) Circle
(d) None of these of rotation

Answer:

The rhombus has only 2 lines of symmetry.


Hence, the correct answer is option (b)

Page No 18.17:

Question 2:

Which of the following is/are point symmetric?
(a) Rectangle
(b) Square
(c) Parallelogram
(d) All of these

Answer:

A point of symmetry is a point that represents a "center" of sorts for the figure.
Hence, the correct answer is option (d)



Page No 18.18:

Question 3:

Which of the following has an infinite number of lines of symmetry?
(a) Equilateral triangle
(b) Isosceles triangle
(c) Regular hexagon
(d) Circle

Answer:

A circle has infinite number of lines of symmetry

Hence, the correct answer is option (d).

Page No 18.18:

Question 4:

Which of the following is point symmetric?
(a) Equilateral triangle
(b) Trapezium
(c) Rectangle
(d) None of these

Answer:

A point of symmetry is a point that represents a "center" of sorts for the figure.
Hence, the correct answer is option (c)

Page No 18.18:

Question 5:

The number of lines of symmetry of a square is
(a) 2
(b) 3
(c) 4
(d) Infinite

Answer:

The number of lines of symmetry of a square is 4.

Hence, the correct answer is option (c).

Page No 18.18:

Question 6:

The number of lines of symmetry of a rectangle is
(a) 2
(b) 3
(c) 4
(d) 1

Answer:

The number of lines of symmetry of a rectangle is 2

Hence, the correct answer is option (a).

Page No 18.18:

Question 7:

The number of lines of symmetry of an equilateral triangle is
(a) 1
(b) 2
(c) 3
(d) 0

Answer:

The number of lines of symmetry of an equilateral triangle is 3

Hence, the correct answer is option (c).

Page No 18.18:

Question 8:

The order of rotational symmetry of an equilateral triangle is
(a) 0
(b) 1
(c) 2
(d) 3

Answer:

The order of rotational symmetry of an equilateral triangle is 3 i.e., 120°, 240° and 360°.
Hence, the correct answer is option (d).

Page No 18.18:

Question 9:

A rectangle has rotational symmetry of order
(a) 1
(b) 2
(c) 3
(d) 4

Answer:

A rectangle has order of rotational symmetry of 2 i.e., 180° and 360°
Hence, the correct answer is option (b).

Page No 18.18:

Question 10:

The number of lines of symmetry of an isosceles triangle is
(a) 0
(b) 1
(c) 2
(d) 3

Answer:

The number of lines of symmetry of an isosceles triangle is 1

Hence, the correct answer is option (b).



Page No 18.6:

Question 1:

State the number of lines of symmetry for the following figures:
(i) An equilateral triangle
(ii) An isosceles triangle
(iii) A scalene triangle
(iv) A rectangle
(v) A rhombus
(vi) A square
(vii) A parallelogram
(viii) A quadrilateral
(ix) A regular pentagon
(x) A regular hexagon
(xi) A circle
(xii) A semicircle

Answer:

(i) An equilateral triangle has 3 lines of symmetry.
(ii) An isosceles triangle has 1 line of symmetry.
(iii) A scalene triangle has no line of symmetry.
(iv) A rectangle has 2 lines of symmetry.
(v) A rhombus has 2 lines of symmetry.
(vi) A square has 4 lines of symmetry.
(vii) A parallelogram has no line of symmetry.
(viii) A quadrilateral has no line of symmetry.
(ix) A regular pentagon has 5 lines of symmetry.
(x) A regular hexagon has 6 lines of symmetry.
(xi) A circle has an infinite number of lines of symmetry all along the diameters.
(xii) A semicircle has only one line of symmetry.



Page No 18.7:

Question 2:

What other name can you give to the line of symmetry of
(i) An isosceles triangle?
(ii) A circle?

Answer:

(i) An isosceles triangle has only 1 line of symmetry.
    
   This line of symmetry is also known as the altitude of an isosceles triangle.

(ii) A circle has an infinite number of lines of symmetry all along its diameters.
     

Page No 18.7:

Question 3:

Identify three examples of shapes with no line of symmetry.

Answer:

A scalene triangle, a parallelogram and a trapezium do not have any line of symmetry.

Page No 18.7:

Question 4:

Identify multiple lines of symmetry, if any, in each of the following figures:

Answer:

(A) The given figure has 3 lines of symmetry. Therefore it has multiple lines of symmetry.
     
(B) The given figure has 2 lines of symmetry. Therefore it has multiple lines of symmetry.
     
(C) The given figure has 3 lines of symmetry. Therefore it has multiple lines of symmetry.
     
(D) The given figure has 2 lines of symmetry. Therefore it has multiple lines of symmetry.
     
(E) The given figure has 4 lines of symmetry. Therefore it has multiple lines of symmetry.
     
(F) The given figure has only 1 line of symmetry.
    
(G) The given figure has 4 lines of symmetry. Therefore it has multiple lines of symmetry.
      
(H) The given figure has 6 lines of symmetry. Therefore it has multiple lines of symmetry.
     



Page No 18.8:

Question 1:

In the following figures, the mirror line (i.e. the line of symmetry) is given as dotted line. Complete each figure performing reflection in the dotted (mirror) line. Also, try to recall the name of the complete figure.

Answer:

(a) It will be a square.
     
(b) It will be a triangle.
     
(c) It will be a rhombus.
    
(d) It will be a circle.
     
(e) It will be a pentagon.
    
(f) It will be an octagon.
    



Page No 18.9:

Question 2:

Each of the following figures shows paper cuttings with punched holes. Copy these figures on a plane sheet and mark the axis of symmetry so that if the paper is folded along it, then the wholes on one side of it coincide with the holes on the other side.

Answer:

The lines of symmetry in the given figures are as follows:
(a)
  
(b)
   
(c)
  
(d)
 
(e)
 
(f)
  
(g)
  
(h)
 
(i)
 
(j)
 
(k)
 
(l)
 

Page No 18.9:

Question 3:

In the following figures if the dotted lines represent the lines of symmetry, find the other hole (s).

Answer:

The other holes in the given figures are as follows:
(a)
   
(b)
   
(c)
   
(d)
   
(e)
   
(f)
   



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