NCERT Solutions for Chapter 14 Symmetry Class 7 Maths
Book Solutions1
Copy the figures with punched holes and find the axes of symmetry for the following:
Answer
S.No. | Punched holed figures | The axes of symmetry |
(a) |
|
(rectangle) |
(b) |
|
(Square) |
(c) |
|
|
(d) |
|
|
(e) |
|
(Square) |
(f) |
|
|
(g) |
|
|
(h) |
|
|
(i) |
|
|
(j) |
|
|
(k) |
|
|
(l) |
|
|
2
Given the line(s) of symmetry, find the other hole(s):
S.No. | Line(s) of symmetry | Other holes on figures |
(a) |
| |
(b) |
| |
(c) |
| |
(d) |
| |
(e) |
| |
Answer
S.No. | Line(s) of symmetry | Other holes on figures |
(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).
(a)
Answer
S.No. | Question figures | Complete figures | Names of the figure |
(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) 
(c) 
Identify multiple lines of symmetry, if any, in each of the following figures:
Answer
S.No. | Problem Figures | Lines of symmetry |
(a) |
|
|
(b) |
|
|
(c) |
|
|
(d) |
|
|
(e) |
|
|
(f) |
|
|
(g) |
|
|
(h) |
|
|
5
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?
Answer
figures are:
Yes, there is more than one way.
6
Copy the diagram and complete each shape to be symmetric about the mirror line (s) :
Answer
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
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 |
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
Answer
(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
Mirror 
(c) Both horizontal and vertical mirror – H, I, O and X
9
Answer
The three examples are:1. Quadrilateral
2. Scalene triangle
3. Parallelogram
10
(a) an isosceles triangle?
(b) a circle?
Answer
(a) The line of symmetry of an isosceles triangle is median or altitude.(b) The line of symmetry of a circle is diameter.
1
Answer
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.2
Answer
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 |
1
Answer
Circle and Square.2
Draw, wherever possible, a rough sketch of:
(i) a triangle with both line and rotational symmetries of order more than one.
(ii) a triangle with only line symmetry and no rotational symmetry of order more than one.
(iii) a quadrilateral with a rotational symmetry of order more than one but not a line symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than one.
Answer
(i) An equilateral triangle has both line and rotational symmetries of order more than one.
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:
3
Answer
Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.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 |
|
|
|
Answer
|
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∘ |
5
Answer
Square has both line and rotational symmetry of order more than 1.Line symmetry:
Rotational symmetry:
6
Answer
Other angles will be 120∘,180∘,240∘,300∘,360∘
For rotation: It will rotate six times.
For rotation:It will rotate three times. 
For rotation:It will rotate two times.
For rotation:It will rotate one time.
7
Can we have a rotational symmetry of order more than 1 whose angle of rotation is:
(i) 45∘
(ii) 17∘ ?
Answer
(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∘.