NCERT Solutions for Class 7 Maths Chapter 12 Symmetry

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer:

The axes of symmetry are as shown :

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

Answer: The other holes from the symmetry are as shown :

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 completed?

Answer:

The complete figures are as shown :

(a) square (b)triangle (c)rhombus

(c) circle (d) pentagon (e) Octagon

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

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

Answer:

The lines of symmetry of figures are:

(a)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.

(b) There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.

(c)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.

(d)There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.

(e)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.

(f)There is 1 line of symmetry.

(g)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.

(h)There are 6 lines of symmetry. Thus, it has multiple lines of symmetry.

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 diagonals?

Answer: The figure with symmetry may be as shown :

The figure with symmetry may be as shown :

Yes, there is more than one way.

Yes, the figure is symmetric about both the diagonals

Yes, there is more than one way.

Yes, the figure is symmetric about both the diagonals

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

Answer: The complete shapes symmetric about the mirror line(s) are :

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

Answer:

(a) An equilateral triangle

The number of lines of symmetry = 3

(b) An isosceles triangle

The number of lines of symmetry = 1

(c) A scalene triangle

The number of lines of symmetry = 0

(d) A square

The number of lines of symmetry = 4

(e) A rectangle

The number of lines of symmetry = 2

(f) A rhombus

The number of lines of symmetry = 2

(g) A parallelogram

The number of lines of symmetry = 0

(h) A quadrilateral

The number of lines of symmetry = 0

(i) A regular hexagon

The number of lines of symmetry = 6

(j) A circle

The number of lines of symmetry = infinite

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

(a) a vertical mirror

(b) a horizontal mirror

(c) Both horizontal and vertical mirrors

Answer: (a) a vertical mirror: A, H, I, M, O, T, U, V, W, Xand Y

(b) horizontal mirror: B, C, D, E, H, I, O and X

(c) both horizontal and vertical mirrors: H, I, O and X.

Question: 9 Give three examples of shapes with no line of symmetry.

Answer: The three examples of shapes with no line of symmetry are :

1. Quadrilateral

2. Scalene triangle

3. Parallelogram

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

Answer: The line of symmetry of an isosceles triangle is median or altitude.

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

a circle?

Answer: The other name we can give to the line of symmetry of a circle is the diameter.

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

Answer: Among the above-given shapes, (a),(b), (d),(e) and (f) have more than one rotational symmetry.

This is because, in these figures, a complete turn, more than 1 number of times, an object looks exactly the same.

Question: 2 Give the order of rotational symmetry for each figure:

Answer: (a) The given figure has a rotational symmetry of about ${180}^{\circ }$, so it is ordered as 2.

(b) The given figure has rotational symmetry about ${180}^{\circ }$, so it has ordered as 2.

(c) The given figure has rotational symmetry about ${120}^{\circ }$, so it has ordered as 3.

(d) The given figure has rotational symmetry about ${90}^{\circ }$, so it has ordered as 4.

(e) The given figure has rotational symmetry about ${90}^{\circ }$, so it has ordered as 4.

(f) The given figure has rotational symmetry about ${72}^{\circ }$, so it has ordered as 5.

(g) The given figure has rotational symmetry about ${60}^{\circ }$, so it has ordered as 6.

(h) The given figure has rotational symmetry about ${120}^{\circ }$, so it has ordered as 3.

Question: 1 Name any two figures that have both line symmetry and rotational symmetry

Answer: The two figures that have both line symmetry and rotational symmetry are :

(i) Equilateral triangle

(ii) Regular hexagon

Question: 2 (i) Draw, wherever possible, a rough sketch of

a triangle with both line and rotational symmetries of order more than 1.

Answer:

Line of symmetry is shown below :

The rotational symmetry is shown below :

Question: 2 (ii) Draw, wherever possible, a rough sketch of

a triangle with only line symmetry and no rotational symmetry of order more than 1.

Answer: A triangle with only line symmetry and no rotational symmetry of order more than 1 is an isosceles triangle.

Question: 2 (iii) Draw, wherever possible, a rough sketch of

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 is a parallelogram.

Question: 2 (iv) Draw, wherever possible, a rough sketch of

a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Answer: A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is a kite.

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 should have rotational symmetry of order more than 1.

Question: 4 Fill in the blanks:
$\begin{array}{|llll|}\hline \text{ Shape }& \begin{array}{c}\text{ Centre of }\\ \text{ Rotation }\end{array}& \begin{array}{c}\text{ Order of }\\ \text{ Rotation }\end{array}& \begin{array}{c}\text{ Angle of }\\ \text{ Rotation }\end{array}\\ \text{ Square }& & & \\ \text{ Rectangle }& & & \\ \text{ Rhombus }& & & \\ \begin{array}{c}\text{ Equilateral }\\ \text{ Triangle }\end{array}& & & \\ \text{ Regular Hexagon }& & & \\ \text{ Circle }& & & \\ \text{ Semi-circle }& & & \\ \hline\end{array}$

Answer: The given table is completed as shown:
$\begin{array}{|llll|}\hline \text{ Shape }& \text{ Centre of Rotation }& \begin{array}{c}\text{ Order of }\\ \text{ Rotation }\end{array}& \begin{array}{c}\text{ Angle of }\\ \text{ Rotation }\end{array}\\ \text{ Square }& \begin{array}{c}\text{ the intersection point of }\\ \text{ diagonals. }\end{array}& 4& {90}^{\circ }\\ \text{ Rectangle }& \begin{array}{c}\text{ The intersection point of }\\ \text{ diagonals. }\end{array}& 2& {180}^{\circ }\\ \text{ Rhombus }& \begin{array}{c}\text{ The intersection point of }\\ \text{ diagonals. }\end{array}& 2& {180}^{\circ }\\ \begin{array}{c}\text{ Equilateral }\\ \text{ Triangle }\end{array}& \begin{array}{c}\text{ The intersection point of }\\ \text{ medians. }\end{array}& 3& {120}^{\circ }\\ \text{ Regular Hexagon }& \begin{array}{c}\text{ The intersection point of }\\ \text{ diagonals. }\end{array}& 6& {60}^{\circ }\\ \text{ Circle }& \text{ centre of circle }& \text{ infinite }& \text{ any angle }\\ \text{ Semi-circle }& \text{ centre of circle }& 1& {360}^{\circ }\\ \hline\end{array}$

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

Answer: The quadrilaterals which have both line and rotational symmetry of order more than 1 are :

1. Rectangle

2. Square

3. Rhombus

Question: 6 After rotating by ${60}^0$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Answer: After rotating by ${60}^0$ about a centre, a figure looks exactly the same as its original position, then it will look symmetrical on rotating by ${120}^{\circ },{180}^{\circ },{240}^{\circ },{300}^{\circ },{360}^{\circ }.$ All angles are multiples of ${60}^0$ .

Question: 7 Can we have a rotational symmetry of order more than 1 whose angle of rotation is:

$(i){45}^o?$$(ii){17}^o?$

Answer: We can observe that the angle of rotation is the factor of ${360}^{\circ }$, then it will have rotational symmetry of order more than 1.

(i) ${45}^o$ is a factor of ${360}^{\circ }$ so the figure having its angle of rotation as ${45}^o$ will have rotational symmetry of order more than 1.

(ii) ${17}^o$ is not a factor of ${360}^{\circ }$ so the figure having its angle of rotation as ${17}^o$ will not have rotational symmetry of order more than 1.