The angle of rotation in equilateral triangle is
- A$60^{\circ}$
- B$70^{\circ}$
- C$90^{\circ}$
- ✓$120^{\circ}$
Answer: D.
View full solution →Question types
Symmetry question types
81 questions across 10 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
81
Questions
10
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
10 Q→02Assertion (A) & Reason (B) MCQ
4 Q→03True False[1 Marks ]
5 Q→04BLANKS [1 Marks Each]
5 Q→051 Marks Question
22 Q→062 Marks Questions
16 Q→075 Marks Questions
7 Q→08case /data -based (4 Marks)
3 Q→09Match the following.
1 Q→103 Marks Question
8 Q→Sample Questions
Symmetry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The angle of rotation for the figure given below is
- A$45^{\circ}$
- B$60^{\circ}$
- ✓$90^{\circ}$
- D$180^{\circ}$
Answer: C.
View full solution →The order of rotational symmetry in the figure given below is
- A4
- ✓2
- C1
- Dinfinitely many
Answer: B.
View full solution →The order of rotational symmetry in the figure given below is
- A4
- B8
- ✓6
- Dinfinitely many
Answer: C.
View full solution →The number of lines of symmetry in the figure given below is
- A4
- B8
- ✓6
- Dinfinitely many
Answer: C.
View full solution →Assertion (A) Out of the ten numerical digits from 0 to 9 , only two digits show rotational symmetry.
Reason (R) In a complete turn, the number of times, a figure coincides with its original position is called its order of rotational symmetry.
Reason (R) In a complete turn, the number of times, a figure coincides with its original position is called its order of rotational symmetry.
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion (A) E has an horizontal line of symmetry.
Reason (R) The symmetry of an object is defined as one half of the object is a mirror image of the other half.
Reason (R) The symmetry of an object is defined as one half of the object is a mirror image of the other half.
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion (A) The letter O has many lines of symmetry.
Reason (R) Line passing through the centre of O, will be its line of symmetry.
Reason (R) Line passing through the centre of O, will be its line of symmetry.
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →Assertion (A) An equilateral triangle has three lines of symmetry.
Reason (R) The number of lines of symmetry in a regular polygon with side (n) is equal to n.
Reason (R) The number of lines of symmetry in a regular polygon with side (n) is equal to n.
- ✓Both A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- DA is false but R is true.
Answer: A.
View full solution →A parallelogram has two lines of symmetry.
A circle has two lines of symmetry.
An equilateral triangle has six lines of symmetry.
Order of rotational symmetry of a semi-circle is two.
The number of line of symmetry of a regular polygon is equal to the vertices of the polygon.
Order of rotational symmetry of a circle is __________ .
__________ triangle is a figure that has a line of symmetry, but lacks rotational symmetry.
In an isosceles right angled triangle, the number of lines of symmetry is __________ .
Each of the letters H, N, S and Z has a rotational symmetry of order __________ .
Rotation turns an object about a fixed point. This fixed point is called __________ .
Name any two figures that have both line symmetry and rotational symmetry.
Identify multiple lines of symmetry, if any, in each of the following figures.
Identify multiple lines of symmetry, if any, in each of the following figures.
Identify multiple lines of symmetry, if any, in each of the following figures.
Identify multiple lines of symmetry, if any, in each of the following figures.
Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) $45^{\circ}$ ?
(ii) $17^{\circ}$ ?
View full solution →(i) $45^{\circ}$ ?
(ii) $17^{\circ}$ ?
After rotating by $60^{\circ}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
View full solution →Name the quadrilateral which have both line and rotational symmetry of order more than 1.
If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
(i) In the given figure, can you now tell the order of the rotational symmetry for an equilateral triangle?
(ii) How many positions are there at which the triangle looks exactly the same, when rotated about its centre by $120^{\circ} ?$
View full solution →(ii) How many positions are there at which the triangle looks exactly the same, when rotated about its centre by $120^{\circ} ?$
Fill in the blanks.
| Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
| Square | |||
| Rectangle | |||
| Rhombus | |||
| Equilateral triangle | |||
| Regular hexagon | |||
| Circle | |||
| Semi-circle |
Some of the English alphabets have fascinating symmetrical structures. Which capital letters have just one line of symmetry (like E)? Which capital letters have a rotational symmetry of order 2 (like I)?
By attempting to think on such lines, you will be able to fill in the following table.
By attempting to think on such lines, you will be able to fill in the following table.
| Alphabet Letters | Line Symmetry | Number of Lines of Symmetry | Rotational Symmetry | Order of Rotational Symmetry |
| Z | No | 0 | Yes | 2 |
| S | ||||
| H | Yes | Yes | ||
| O | Yes | Yes | ||
| E | Yes | |||
| N | Yes | |||
| C |
Give the order of rotational symmetry for each figure.
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
(ix) A circle
(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
(ix) A circle
In each of the following figures, write the number of lines of symmetry and order of rotational symmetry.
Here is a picture of a car wheel.
What is the order of rotational symmetry for this wheel?
What is the order of rotational symmetry for this wheel?
A quadrilateral is drawn on a square grid. $O$ is the dot marked on one vertex of the quadrilateral.
Q. 1. How many lines of symmetry are there in this quadrilateral?
(a) 0 $\quad$ (b) 1 $\quad$ (c) 2 $\quad$ (d) 4
Q. 2. Draw three more congruent quadrilaterals around 0 so that the complete figure has rotational symmetry of order four.
Q. 3. Which of the following statements about a parallelogram's symmetry is true?
(a) A parallelogram has neither a line of symmetry nor rotational symmetry,
(b) A parallelogram has a line of symmetry but no rotational symmetry.
(c) A parallelogram has a point symmetry and rotational symmetry but no line of symmetry.
(d) A parallelogram has rotational symmetry but no point or line symmetry.
Q. 4. Jyoti claims that rotational symmetry of order 1 implies no rotational symmetry. Do you agree or disagree with her claim? Give reasons.
View full solution →Q. 1. How many lines of symmetry are there in this quadrilateral?
(a) 0 $\quad$ (b) 1 $\quad$ (c) 2 $\quad$ (d) 4
Q. 2. Draw three more congruent quadrilaterals around 0 so that the complete figure has rotational symmetry of order four.
Q. 3. Which of the following statements about a parallelogram's symmetry is true?
(a) A parallelogram has neither a line of symmetry nor rotational symmetry,
(b) A parallelogram has a line of symmetry but no rotational symmetry.
(c) A parallelogram has a point symmetry and rotational symmetry but no line of symmetry.
(d) A parallelogram has rotational symmetry but no point or line symmetry.
Q. 4. Jyoti claims that rotational symmetry of order 1 implies no rotational symmetry. Do you agree or disagree with her claim? Give reasons.
Match the Column A to Column B.
View full solution →| Column A | Column B |
| (i) A half-turn means rotation by | (a) $180^{\circ}$ |
| (ii) A quarter-turn means rotation by | (b) sides and angles |
| (iii) A complete turn means rotation by | (c) $90^{\circ}$ |
| (iv) Regular polygon have equal | (d) $360^{\circ}$ |
Give the order of the rotational symmetry of the given figures about the point marked x.
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.
(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.
Which of the following figures have rotational symmetry of order more than 1:
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?
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?
In the following figures, the mirror line (L.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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