Chapter -14 Symmetry | Class 7th |NCERT Maths Solutions | Edugrown

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.

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

(b)

(c)

(d)

(e)

(f)

Solution:
Figures (a), (b), (d), (e), and (f) have rotational symmetry of order more than 1.

Question 2.
Give the order of rotational symmetry for each figure :
(a)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

(b)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

(c)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

(d)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

(e)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

(f)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

(g)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

(h)

Solution:
Let us mark a point A on each figure and also indicate the angle through which the figure is to be rotated as under :

Now to find the rotational symmetry, we proceed as under :

In figure (a): it requires two rotations, each through an angle of 180°, about the marked point (x) to come back to its original position. So, its rotational symmetry is of order 2.

In figure (b): It requires two rotations, each through an angle of 180°, about the marked point (x) to come back to its original position. So, its rotational symmetry is of order 2.

In figure (c): The triangle requires three rotations, each through an angle of 120° about the marked point to come back to its original position. So, it has rotational symmetry of order 3.

In figure (d): The figure requires four rotations, each through an angle of 90°, about the marked point (x) to come back to its original position. So, its rotational symmetry is of order 4.

n figure (e): The figure requires four rotations, each through an angle of 90°, about the marked point (x) to come back to its original position. So, its rotational symmetry is of order 4.

In figure (f): The regular pentagon requires five rotations, each through an angle of 72°, about the marked point to come back to its original position. So, it has rotational symmetry of order 5.

In figure (g): The figure requires six rotations, each through an angle of 60°, about the marked point to come back to its original position. So, it has rotational symmetry of order 6.

In figure (h): The figure requires three rotations each through an angle of 120°, about the marked point to come back to its original position. So, it has rotational symmetry of order 3.

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

1. Circle
2. Equilateral triangle

Question 2.
Draw, wherever possible, a rough sketch of
(i) a triangle with both line and rotational symmetries of order more than 1.
Solution:
Three lines of symmetry

Also, an equilateral triangle has rotational symmetry of order 3 as shown below:

(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.
Solution:
One line of symmetry but no rotational symmetry of order more than 1.

(iii) a quadrilateral with rotational symmetry of order more than 1 but not a line symmetry.
Solution:
No line of symmetry but have rotational symmetry of order more than 1.

(iv) a quadrilateral with line symmetry but not a rotational symmetry or order more than 1.
Solution:
One line of symmetry but no rotational symmetry of order more than 1.

Question 3.
If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Solution:
When a figure has two or more lines of symmetry, then the figure should have rotational symmetry of order more than 1.

Question 4.
Fill in the blanks:

Shape	Centre of Rotation	Order of Rotation	Angle of Rotation
Square
Rectangle
Rhombus
Equilateral Triangle
Regular Hexagon
Circle
Semicircle

Solution:

Shape	Centre of Rotation	Order of Rotation	Angle of Rotation
Square	Yes	4	90°
Rectangle	Yes	4	90°
Rhombus	Yes	4	90°
Equilateral Triangle	Yes	3	120°
Regular Hexagon	Yes	6	60°
Circle	Yes	Infinite	Any angle
Semicircle	Yes	4	90°

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

1. Square
2. Rectangle

Question 6.
After rotating by 60° about a center, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Solution:
The other angles are 120°, 180°, 240°, 300°, 360°.

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

(i) 45°?
Solution:
Yes

(ii) 17°?
Solution:
No