Class – 7 CH-14 SYMMETRY MATHS NCERT SOLUTIONS

 

Class – 7 CH-14 SYMMETRY 

MATHS NCERT SOLUTIONS

 Exercise 14.1 

       

Question 1:   

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

 

 

S.No. Punched holed figures The axes of symmetry 

(a)   (rectangle) 

(b)     

 

(c)     

(d)     

(e)     

(f)     

(g)     

(h)     

(i)     

(j)     

(k)     

(l)     

 

 

Question 2:   

Express the following in exponential form: 

 

 

 

  SOLUTION 2:  

S.No. Line(s) of symmetry Other holes on figures 

(a)     

(b)     

(c)     

(d)     

(e)     

 

 

Question 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) 

  SOLUTION 3:  

S.No. Question figures Complete figures Names of the figure 

(a)     Square 

(b)     Triangle 

(c)     Rhombus 

(d)     

Circle 

 

(e)     Pentagon 

(f)     Octagon 

 

  

Question 4:   

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

 

 

 

 

  SOLUTION 4:  

S.No. Problem Figures Lines of symmetry 

(a)     

(b)     

(c)     

(d)     

(e)     

(f)     

(g)     

(h)     

 

 

Question 5:   

Copy the figure given here: 

Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals? 

   

   

   

   

  SOLUTION 5:  

SOLUTION figures are: 

  

Yes, there is more than one way. 

Yes, this figure will be symmetric about both the diagonals. 

 

 

 

Question 6:   

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

  

  (a)    (b)       (c)  (d) 

  SOLUTION 6:  

   

Question 7:   

State the number of lines of symmetry for the following figures: 

(a) An equilateral triangle (b) An isosceles triangle (c) A scalene triangle 

(d) A square (e) A rectangle (f) A rhombus 

(g) A parallelogram (h) A quadrilateral (i) A regular hexagon 

(j) A circle   SOLUTION 7:  

S.No. Figure’s name Diagram with symmetry Number of lines 

(a) Equilateral triangle   3 

(b) Isosceles triangle   1 

(c) Scalene triangle   0 

(d) Square   4 

(e) Rectangle   2 

(f) Rhombus   2 

(g) Parallelogram   0 

(h) Quadrilateral   0 

(i) Regular Hexagon   6 

(j) Circle   Infinite 

 

 

Question 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   SOLUTION 8:  

(a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y 

            mirror                mirror 

                             

(b) Horizontal mirror – B, C, D, E, H, I, O and X 

   

 

(c) Both horizontal and vertical mirror – H, I, O and X  

Question 9:   

Give three examples of shapes with no line of symmetry. 

  SOLUTION 9:  

The three examples are: 

 Quadrilateral 

 Scalene triangle 

 Parallelogram 

 

Question 10:   

What other name can you give to the line of symmetry of: (a) an isosceles triangle? (b) a circle?   SOLUTION 10:  

(a) The line of symmetry of an isosceles triangle is median or altitude. 

(b) The line of symmetry of a circle is diameter. 

 

 Exercise 14.2  

Question 1:   

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

 

  

(d) (e) (f) 

Rotational symmetry of order more than 1 are a,b,d,e and  f  because in these figures, a complete turn, more than 1 number of times, an object looks exactly the same. 

 

 

Question 2:   

Give the order the rotational symmetry for each figure: 

    

       (f)       (g)            (h) 

S.No. Problem figures Rotational figures Order of rotational symmetry 

(a)     2 

(b)     2 

(c)     3 

(d)     4 

(e)     4 

(f)    

  5 

(g)     6 

(h)     3 

 

 

 

 Exercise 14.3  

Question 1:   

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

  SOLUTION 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. 

  SOLUTION 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) It is not possible because order of rotational symmetry is more than 1 of a figure, most acertain the line of symmetry. 

(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?   SOLUTION 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  

Rectangle  

Rhombus  

Equilateral triangle  

Regular hexagon  

Circle  

Semi-circle  

  SOLUTION 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. 

  SOLUTION 5:  

Square has both line and rotational symmetry of order more than 1. 

 

 

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? 

  SOLUTION 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) 45  (ii) 17 ? 

  SOLUTION 7:  

(i) If the 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 of order is not possible because 360 is not complete divided by 17 .