NCERT Solutions of Chapter: Symmetry. NCERT Solutions along with worksheets and notes for Class 7.

 

Exercise 14.1

(1)Copy the figures with punched holes and find the axes of symmetry for the following:

 

 

                                 

      (a)                                                       (b)                                                   (c)

 

                               

     (d)                                                 (e)                                                               (f) 

 

                         

(g)                                                                    (h)

 

      

 (i)                                                                    (j) 

 

                             

 (k)                                                                             (l)   

 

 

Ans-Axes of symmetry for figures are given below:-

(a)

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

Note:-

Line of symmetry can be only one if line passing through punched holes (red) and line passing through center of the figure (blue) do not coincide.

                                     

(b)

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

(c)

 

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

 

(d)

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

(e)

 

Line of symmetry = 4

Mirror reflections of the punches can be received in above 4 positions of line of symmetry because one half of the figure is exactly mirror images of the other half of the figure.

 

(f)

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

(g)

 

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

(h)

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

(i)

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

(j)

 

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

 

(k)

 

Line of symmetry = 2

Mirror reflections of the punches can be received in above 2 positions of line of symmetry because one half of the figure is exactly mirror images of the other half of the figure.

(l)

Line of symmetry = 1

Mirror reflections of the punches can be received only in above position of line of symmetry because one half of the figure is exactly mirror image of the other half of the figure.

 

(2)Given the line(s) of symmetry, find the other hole(s):

 

                           

  (a)                                                                                                (b)

 

                         

(c)                                                                                    (d)

 

 (e)

 

Ans- The position of other hole(s) is given below:-

(a)

 

(b)

 

(c)

 

(d)

 

 

(e)

 

(3)In the following figures, the mirror line (i.e., the line of symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete?

 

                                                                  

    (a)                                                        (b)                                        (c)

 

                                                                                 

        (d)                                                       (e)                                          (f)   

 

Ans-        

 

(a)

Square

 

(b)

 

Triangle

 

(c)

Rhombus

 

(d)

 

Circle

 

(e)

Pentagon

 

(f)

Octagon

 

(4)The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.

 

                       (a)

 

                                (b)

 

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

 

 

                       

    (a)                                                                     (b) 

 

                

(c)                                                                      (d)

 

                                       

   (e)                                                                               (f)

 

                                   

(g)                                                                       (h)

 

Ans-

(a)

This figure has three lines of symmetry. Therefore, it has multiple lines of symmetry.

(b)

This figure has two lines of symmetry. Therefore, it has multiple lines of symmetry.

(c)

This figure has three lines of symmetry. Therefore, it has multiple lines of symmetry.

(d)

This figure has two lines of symmetry. Therefore, it has multiple lines of symmetry.

(e)

This figure has four lines of symmetry. Therefore, it has multiple lines of symmetry.

(f)

This figure has one line of symmetry. Therefore, it does not have multiple lines of symmetry.

(g)

This figure has four lines of symmetry. Therefore, it has multiple lines of symmetry.

(h)

This figure has six lines of symmetry. Therefore, it has multiple lines of symmetry.

 

Ans-

  (a)

 

 

                       (b)

 

Yes, figure will be symmetric about both the diagonal.

 

(6) Copy the diagram and complete each shape to be symmetric about the mirror line(s):

 

(a)

 

 

(b)

 

 

  (c)

 

 

Ans-

Diagrams of each shape symmetrical about the mirror line(s) are showing below:

(a)

 

 

(b)

 

 

(c)

 

 

(d)

 

 

Ans-

(a) An equilateral triangle

Lines of symmetry = 3

 

(b) An isosceles triangle

Lines of symmetry =1

 

(c) A scalene triangle

Lines of symmetry =0

Note- All sides of a scalene triangle are unequal. Therefore, scale triangle does not have any line of symmetry.

(d)A square

Lines of symmetry=4

(e) A rectangle

Lines of symmetry=2

(f) A rhombus

Lines of symmetry=4

 

(g) A parallelogram

Lines of symmetry=0

 

(h) A quadrilateral

Lines of symmetry=0

 

(i) A regular hexagon

Lines of symmetry=6

 

 

(j) A circle

Lines of symmetry=infinity

 

(8)What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about.

(a) a vertical mirror  (b) a horizontal mirror  (c)both horizontal and vertical mirrors

Ans-

(i)

A

(ii)

 

H

(iii)

 

I

(iv)

 

M

(v)

 

O

(vi)

T

(vii)

U

(viii)

V

(ix)

W

(x)

X

(xi)

Y

(b)  Letters of the English alphabet have reflectional symmetry about a horizontal mirror.

 

(i)

B

(ii)

C

(iii)

D

(iv)

E

(v)

H

(vi)

I

(vii)

O

(viii)

X

(c) ) Letters of the English alphabet have reflectional symmetry about both horizontal and vertical mirrors.

(i)

O

(ii)

X

(iii)

I

(iv)

H

(9) Give three examples of shapes with no line of symmetry.

Ans-

(i) A parallelogram

(ii) A quadrilateral

(iii)A scalene triangle

 

 

(10)What other name can you give to the line of symmetry of

(a) an isosceles triangle? (b) a circle?

Ans-

(a) The other name for the line of symmetry of an isosceles triangle is median.

(b) The other name for the line of symmetry of a circle is diameter.

 

Exercise 14.2

(1)Which of the following figures have rotational symmetry of order more than 1:

 

 

                                    

                                                                     

                                                                     

                                                                                

                             

                                                                                  

Ans-

(a)

(b)

(c)

(d)

 

(e)

(f)

                  

(a)                                                     (b)

 

                   

(c)                                                         (d)

 

                                    

(e)                                                                             (f)

 

                                   

(g)                                                                   (h)

 

Ans-

(a)

 

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Exercise 14.3

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

Ans-

(i)Equilateral Triangle

Line symmetry-

Hence,line symmetry is 3.

Rotational symmetry-

 

Line symmetry-

Hence,line symmetry is 6.

Rotational symmetry-

Hence,rotational symmetry is 6.

 

(2)Draw, whenever 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 a line symmetry but not a rotational symmetry of order more than 1.

Ans-

(i)A equilateral triangle has line symmetry and rotational symmetry of order 3.

Line symmetry-

Hence,line symmetry is 3.

Rotational symmetry-

Hence,rotational symmetry is order of 3.

(ii)A isosceles triangle has line symmetry and rotational symmetry of order 1.

 

Line symmetry-

Hence,line symmetry is 1.

Rotational symmetry-

 

Hence,rotational symmetry is order of 1.

(iii)A parallelogram has a rotational symmetry of order more than 1 but not a line symmetry.

Line symmetry

                                               

Line of symmetry divides parallelogram                    No mirror image of two parts

Hence, no line of symmetry.

Rotational symmetry-

 

 

Hence,rotational symmetry is 2.

(iv)A kite is a quadrilateral with a line symmetry but not a rotational symmetry of order more than 1.

Line symmetry

Hence,line symmetry is 1.

Rotational symmetry-

 

Hence, rotational symmetry is 1.

 

(3)If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1.

Ans-Yes, if a figure has two or more lines of symmetry, it should have rotational symmetry of order more than 1.

 

(5)Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

Ans-

(a) Square

Line of symmetry = 4

Order of rotational symmetry= 4

(b) Rectangle

Line of symmetry = 2

Order of rotational symmetry= 2

(c)Rhombus

Line of symmetry = 2

Order of rotational symmetry= 2

 

(6)After rotating by 60^o about a center, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Ans- After rotating by 60^o about a center, a figure looks exactly the same as its original position. So we can rotate it by multiples of 60^o.

Multiples of 60^o =120^o,  180^o,  240^o,  300^o, 360^o

 

(7)Can we have a rotational symmetry of order more than 1 whose angle of rotation is (i) 45^o ?     (ii) 17^o ?

Ans-

(i) 45^o

Condition: For rotational symmetry of order more than 1 the angle should be multiple of 360^o.

Angle 45^o is a multiple of 360^o.

Hence, it has rotational symmetry of order more than 1.

(ii) 17^o

Condition: For rotational symmetry of order more than 1 the angle should be multiple of 360^o.

Angle 17^o is not a multiple of 360^o.

Hence, it does not have rotational symmetry of order more than 1.

 

Helping Topics

Symmetry

Worksheet Class 7