# Chapter 14: Symmetry

Exercise-14.1

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

Solution:

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Q.2. Express the following in exponential form:

Solution:

Q.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:

Q.4. Identify multiple lines of symmetry, if any, in each of the following figures:

Solution:

Q.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? Is the figure symmetric if using both diagonals as lines of symmetry?

Solution:

Yes, there is more than one way. Yes, this figure will be symmetric using both the diagonals.

Q.6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):

Solution:

Q.7. State the number of lines of symmetry for the following figures:

(I) An equilateral triangle

(II) An isosceles triangle

(III) A scalene triangle

(IV) A square

(V) A rectangle

(VI) A rhombus

(VII) A parallelogram

(IX) A regular hexagon

(X) A circle

Solution:

Q.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

Solution:

(a) Vertical mirror – A, H, I, M, O, T, U, V, W, X and Y

(b) Horizontal mirror – B, C, D, E, H, I, O and X

(c) Both horizontal and vertical mirror – H, I, O and X

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

Solution: The three examples are:

(ii)Scalene triangle

(iii)Parallelogram

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

(a) an isosceles triangle?

(b) a circle?

Solution:

(a) The line of symmetry of an isosceles triangle is median or altitude.

(b) The line of symmetry of a circle is diameter.

Class 7th

Chapter-14

Symmetry

Exercise-14.2

Q.1. Which of the following figures have rotational symmetry of order more than 1:

Solution:

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.

Q.2. Give the order the rotational symmetry for each figure:

Solution:

Exercise-14.3

Q.1. Name any two figures that have both line symmetry and rotational symmetry.

Solution: Circle and Square.

Q.2. Draw, wherever possible, a rough sketch of:

(a)A triangle with both line and rotational symmetries of order more than 1.

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

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

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

Solution:

(a)An equilateral triangle has both line and rotational symmetries of order more than 1.

Line symmetry:

Rotational symmetry:

(b) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.

Line symmetry:

Rotational symmetry:

(c) It is not possible because order of rotational symmetry is more than 1.

(d) 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:

Q.3. In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?

Solution: Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.

Q.4. Fill in the blanks:

Solution:

Q.5. Name the quadrilateral that has both line and rotational symmetry of order more than 1.

Solution: Square has both line and rotational symmetry of order more than 1.

Line symmetry:

Rotational symmetry:

Q.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?

Solution: Other angles will be . $$120^{\circ},180^{\circ},240^{\circ},300^{\circ},360^{\circ}$$

For $$60^{\circ}$$ rotation: It will rotate six times.

For $$120^{\circ}$$  rotation: It will rotate three times.

For $$180^{\circ}$$rotation: It will rotate two times.

For $$360^{\circ}$$rotation: It will rotate one time.

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

(i) $$45 ^{\circ}$$

(ii) $$17^{\circ}$$

Solution:

(i)If the angle of rotation is $$45 ^{\circ}$$  , then symmetry of order is possible and would be 8 rotations.

(ii)If the angle of rotational is $$17^{\circ}$$ , then symmetry of order is not possible because $$360^{\circ}$$ is not complete divided by $$17^{\circ}$$ .