NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.1

Class 7 Maths NCERT Solutions Chapter 14 Symmetry Ex 14.1

Question 1.
Copy the figures with punched holes and find the axes symmetry for the following:

(a)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(b)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(c)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(d)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(e)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(f)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(g)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(h)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(i)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(j)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(k)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

(l)

Solution:
The axis of symmetry corresponding to the given punched holes are shown by dotted lines in the figures as under :

Question 2.
Given the lines of symmetry, find the order holes:

(a)

Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:

(b)

Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:

(c)

Sol:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:

(d)

Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:

(e)

Solution:
With the respect to the given lines of symmetry, the order holes are marked in the given figures as order:

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?
Solution:
(a)

Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures:

(b)

Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures:

(c)

Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :

(d)

Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :

(e)

Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :

(f)

Solution:
Corresponding to the given line of symmetry, the completed figure is as under. Their respective names are also given the figures :

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 :
Solution:

(a)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

(b)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

(c)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

(d)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

(e)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

(f)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

(g)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

(h)

solution:
The multiple lines of symmetry in respect of the given figures are shown by dotted lines as under :

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:

Let us mark the vertices of the square as A, B, C and D. Take the diagonal BD as a line of symmetry and shade a few more squares as shown to make the figure symmetric about this diagonal. There is only one way to do it. Clearly, the figure is symmetric about the second diagonal AC. Hence, 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):

(a)

Solution:
Completed shape symmetric about the mirror lines are as under :

(b)

Solution:
Completed shape symmetric about the mirror lines are as under :

(c)

Solution:
Completed shape symmetric about the mirror lines are as under :

(d)

Solution:
Completed shape symmetric about the mirror lines are as under :

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:

	Figure	Number of lines of symmetry
(a)	An equilateral triangle	3
(b)	An isosceles triangle	1
(c)	A scalene triangle	0
(d)	A square	4
(e)	A rectangle	2
(f)	A rhombus	2
(g)	A parallelogram	0
(h)	A quadrilateral	0
(i)	A regular hexagon	6
(j)	A circle	Infinite

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

(a) a vertical mirror
Solution:
The English alphabet letters having reflectional symmetry about a vertical mirror are A, H, I, M, 0, T, U, V, W, X, Y

(b) a horizontal mirror
Solution:
The English alphabet having reflectional symmetry about a horizontal mirror are B, C, D, E, H, I, O, and X

(c) both horizontal and vertical mirrors.
Solution:
The English alphabet having reflectional symmetry about both horizontal and vertical mirrors are H, I, O, and X

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

1. A scalene triangle
2. A parallelogram
3. An irregular quadrilateral

Question 10.
What another name can you give to the line of symmetry of

(a) an isosceles triangle?
Solution:
Another name for the line of symmetry of an isosceles triangle is median.

(b) a circle?
Solution:
Another name for the line of symmetry of a circle is the diameter.