**Exercise-14.1**

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

**Solution:**

1.

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12.

*Q.2. Express the following in exponential form:*

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**Solution:**

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*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?*

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**Solution:**

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

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**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 *

*(VIII) A quadrilateral *

*(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:

(i)Quadrilateral

(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 7^{th}

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:**

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__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 \(17^{\circ}\) .

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