NCERT Solutions for Class 7 Maths Ch 14 Symmetry
Exercise 14.1
1. Copy the figures with punched holes and find the axes of symmetry for the following:
Answer
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?
Answer
(a) Square
(b) Triangle
(c) Rhombus
(d) Circle
(e) Pentagon
(f) Hexagon
4. The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
Answer
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?![Question 5 Exercise 14.1 Class 7 Maths]( "Question 5 Exercise 14.1 Class 7 Maths")
![Answer 5 Exercise 14.1 Class7 Maths]( "Answer 5 Exercise 14.1 Class7 Maths")
![Question 6 Exercise 14.1 Class 7 Maths]( "Question 6 Exercise 14.1 Class 7 Maths")
Answer
Yes, there is more than one way and this figure will be symmetric about both the diagonals.
6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Answer
(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 - Three Lines
(b) An isosceles triangle - Only One Line
(c) A scalene triangle - No Line
(d) A square - Four Lines
(e) A rectangle - Two Lines
(f) A rhombus - Four Lines
(g) A parallelogram - No Line
(h) A quadrilateral - No Line
(i) A regular hexagon - Six Lines
(j) A circle - Infinite Lines
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, 0, T, U, V, W, X and Y
(b) Horizontal mirror - B, C, D, E, H, I, 0 and X
(c) both horizontal and vertical mirrors - O, X,I, H
9. Give three examples of shapes with no line of symmetry.
Answer
The three examples are:
1. Quadrilateral
2. Scalene triangle
3. Parallelogram
10. What other name can you give to the line of symmetry of
(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.
Exercise 14.2
1. Which of the following figures have rotational symmetry of order more than 1:
Rotational symmetry of order more than 1 are (a),(b),(d),(e) and (f).
2. Give the order the rotational symmetry for each figure:
Answer
(a) 2
(b) 2
(c) 3
(d) 4
(e) 4
(f) 5
(g) 6
(h) 3
Exercise 14.3
1. Name any two figures that have both line symmetry and rotational symmetry.
Answer
Circle and Equilateral Triangle.
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.
Answer
(i) An equilateral triangle has both line and rotational symmetries of order more than 1.
(ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.
(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.
3. In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
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. Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer
Square has both line and rotational symmetry of order more than 1.
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?
Answer
After rotating by 60° about a centre, a figure looks exactly the same as its original position. This will happen for the figure at angles 120°, 180°, 240°, 300°, 360° respectively.
7. Can we have a rotational symmetry whose angle of rotation is
(i) 45°?
(ii) 17°?
Answer
(i) Yes
(ii) No.