Class 7 - Maths - Symmetry

**Exercise 14.1**

**Question 1:**

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

Answer:

**Question 2:**

Express the following in exponential form:

Answer:

**Question 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:

**Question 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:

**Question 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:

Answer figures are:

Yes, there is more than one way.

Yes, this figure will be symmetric about both the diagonals.

**Question 6:**

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

Answer:

**Question 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:

**Question 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

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

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

**Question 9:**

Give three examples of shapes with no line of symmetry.

Answer:

The three examples are:

- Quadrilateral 2. Scalene triangle 3. Parallelogram

**Question 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**

**Question 1:**

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

Answer:

Rotational symmetry of order more than 1 are (a), (b), (c), (d), (e) and (f) because in these

figures, a complete turn, more than 1 number of times, an object looks exactly the same.

**Question 2:**

Give the order the rotational symmetry for each figure:

Answer:

**Exercise 14.3**

**Question 1:**

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

Answer:

Two figures that have both line symmetry and rotational symmetry are:

Circle and Square.

**Question 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.

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 a certain 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:

**Question 3:**

If 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.

**Question 4:**

Fill in the blanks:

Answer:

**Question 5:**

Name the quadrilateral which has both line and rotational symmetry of order more than 1.

Answer:

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

Line symmetry:

Rotational symmetry:

**Question 6:**

After rotating by 60^{0} about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Answer 6:

Other angles will be 120^{0} ,180^{0} ,240^{0} ,300^{0} ,360^{0}.

For 60^{0} rotation: It will rotate six times.

For 120^{0} rotation: It will rotate three times.

For 180^{0} rotation: It will rotate two times.

For 360^{0} rotation: It will rotate one time.

**Question 7:**

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

(i) 45^{0} (ii) 17^{0} ?

Answer:

(i) If the angle of rotation is 45^{0}, then symmetry of order is possible and would be 8 rotations.

(ii) If the angle of rotational is 17^{0}, then symmetry of order is not possible because 360^{0} is not

completely divided by 17^{0}.

.