NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Question

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Answer 1

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

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

Answer:

The axis of symmetry is shown by following line.

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

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:

Following are the complete figures.

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:

(a) Figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

(b) Figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

(c) Figure given has 3 lines of symmetry.

So, it has multiple lines of symmetry.

(d) Figure given has 2 lines of symmetry.

So, it has multiple lines of symmetry.

(e) Figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

(f) Figure given has only 1 line of symmetry.

(g) Figure given has 4 lines of symmetry.

So, it has multiple lines of symmetry.

(h) Figure given has 6 lines of symmetry.

So, it has multiple lines of symmetry.

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?

Answer:

(i) Let us take a diagonal as the axis of symmetry and shade the square as shown in the figure.

(ii) Yes, there are more than the line of symmetry i.e. BD, EF and GH.

(iii) Yes, the figure is symmetric about both the diagonals.

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:

(а) 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:

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

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) Alphabet of vertical mirror reflection symmetry are:

A, H, I, M, O, T, U, V, W, X, Y

(b) Alphabet of horizontal mirror reflection symmetry are:

B, C, D, E, H, I, K, O, X

(c) Alphabet of both horizontal and vertical mirror reflection symmetry are:

H, I, O, X.

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

Answer:

A shape has a no line of symmetry, if there is no line about which the figure may be folded and also parts of the figure will not coincide.

A scalene triangle, a quadrilateral and a parallelogram

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

(a) an isosceles triangle?

(b) a circle?

Answer:

(a) The other name to the line of symmetry of an isosceles triangle is median or altitude.

(b) The other name to the line of symmetry of a circle is diameter.

Answer 2

11. Which of the following figures have rational symmetry of order more than 1?

Answer:

The figure (a), (b), (d), (e) and (f) have rotational symmetry more than 1.

12. Give the order of rotational symmetry for each figure:

Answer:

(a) 

The above figure has its rotational symmetry as 2.

(b)

The above figure has its rotational symmetry as 2.

(c)

The above figure has its rotational symmetry as 3.

(d)

The above figure has its rotational symmetry as 4.

(e)

The above figure has its rotational symmetry as 4.

(f)

The above figure has its rotational symmetry as 5.

(g)

The above figure has its rotational symmetry as 6.

(h)

The above figure has its rotational symmetry as 3.

13. Name any two figures that have both line symmetry and rotational symmetry.

Answer:

Equilateral triangle and circle.

14. 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) A triangle with both line and rotational symmetries of order more than 1 is an equilateral triangle.

Line symmetry

Rotational symmetry

(ii) A triangle with only line symmetry and no rotational symmetry of order more than 1 is isosceles triangle.

(iii) A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry is not possible to draw. This is because a quadrilateral with a line symmetry may have rotational symmetry of order one but not more than one.

(iv) A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is a rhombus.

15. 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 will have rotational symmetry of order more than 1.

Answer 3

16. 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	Every angle
Semi-circle	Mid-point of diameter	1	360°

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

Answer:

The quadrilateral which have both line and rotational symmetry of order more than 1 is a square.

Line symmetry:

Rotational symmetry:

18. 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:

The other angles are, 120°, 180°, 240°, 300°, 360°

So, the figure is said to have rotational symmetry about same angle as the first one. Hence, the figure will look exactly the same when rotated by 60° from the last position.

19. Can we have a rotational symmetry of order more than 1 whose angle of rotation is

(i) 45°?

(ii) 17°?

Answer:

(i) Yes. We can have a rotational symmetry of order more than 1 whose angle of rotation is 45^o.

(ii) No. We cannot have a rotational symmetry of order more than 1 whose angle of rotation is 17^o.