We provide symmetry practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on symmetry skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of symmetry Questions

Question No | Questions | Class |
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1 | The image of the point (1,6,3) in the ( operatorname{line} frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) is? A. (1,0,7) в. (7,0,1) c. (2,7,0) D. (-1,-6,-3) | 7 |

2 | How many lines of symmetry are there in a triangle which has all the angles equal? A . 1 B . 2 ( c .3 ) D. 4 | 7 |

3 | Find the order of rotational symmetry of rhombus. A . 4 B. 3 ( c cdot 2 ) ( D ) | 7 |

4 | Find the number of lines of symmetry in the figure. ( A ) B. 2 ( c cdot 3 ) ( D ) | 7 |

5 | What is the smallest number of squares that must be added so that the line PQ becomes a line of symmetry? ( mathbf{A} cdot mathbf{5} ) B. 3 ( c cdot 4 ) ( D ) | 7 |

6 | State the number of lines of symmetry for the following figures (a) An equilateral triangle (b) Isosceles triangle (c) Scalene triangle (d) A square (e) A rectangle (f) ( A ) rhombus (g) A parallelogram (h) A quadrilateral (i) A regular hexagon (j) A circle. | 7 |

7 | Draw, wherever possible, a rough sketch of: A triangle with only line symmetry and | 7 |

8 | How many lines of symmetry does this star have? ( A cdot 2 ) B. 5 ( c cdot 4 ) ( D ) | 7 |

9 | Match the following. Order of rotational symmetry ( (P) ) (i) 5 ( (mathrm{Q}) ) (ii) 2 ( (mathbf{R}) ) (iii) 3 ( (mathbf{S}) ) (iv) 4 ( mathbf{A} cdot(mathrm{P}) rightarrow(mathrm{iv}),(mathrm{Q}) rightarrow(mathrm{i}),(mathrm{R}) rightarrow(mathrm{i}),(mathrm{S}) rightarrow(mathrm{iii}) ) B. ( (P) rightarrow(text { iv) },(Q) rightarrow(text { iii) },(R) rightarrow(text { ii) },(S) rightarrowtext { (i) } ) C. ( (P) rightarrow(text { ii) },(Q) rightarrow(text { iv }),(R) rightarrow(text { iii) },(S) rightarrow(i) ) ( mathbf{D} cdot(mathbf{P}) rightarrow(mathbf{i} mathbf{i}),(Q) rightarrow(mathbf{i}),(R) rightarrow(i mathbf{v}),(S) rightarrow(text { iii }) ) | 7 |

10 | List the coordinates of the vertices of the larger shape | 7 |

11 | Name a triangle which has exactly one line of symmetry. Show line of symmetry in figure. | 7 |

12 | Find the value of the solid obtained by the complete revolution of the ellipse ( frac{x^{2}}{36}+frac{y^{2}}{25}=1 ) about ( x- ) axis. | 7 |

13 | Draw a quadrilateral that have four lines of symmetry. | 7 |

14 | toppr Q Type your question ( A ) B. ( c ) ( D ) | 7 |

15 | Give the order of the rotational symmetry for each figure: | 7 |

16 | The no-of order of rotational symmetry of B, E, D?. | 7 |

17 | Let ( 0<alpha<frac{pi}{2} ) be a fixed angle. If ( P= ) ( (cos theta, sin theta) ) and ( Q=(cos (alpha- ) ( boldsymbol{theta}), sin (boldsymbol{alpha}-boldsymbol{theta})) ) then ( boldsymbol{Q} ) is obtained from ( P ) by A. clockwise rotation around the origin through an angle B. anticlockwise rotation around the origin through an angle ( alpha ) c. reflection in the line through origin with slope ( tan alpha ) D. reflection in the line through the origin with slope ( tan (alpha / 2) ) | 7 |

18 | The number of line symmetries that the given figure have- – ( A ) B. 3 ( c cdot 2 ) D. | 7 |

19 | How many lines of symmetry are there in a regular octagon? | 7 |

20 | Rectangle ABCD is the image of rectangle ABCD after which of the following rotations? A ( cdot ) A ( 90^{circ} ) clockwise rotation about the origin B. A ( 180^{circ} ) rotation about the origin C. ( A 90^{circ} ) counterclockwise rotation about the origin D. A ( 90^{circ} ) counterclockwise rotation about the point (1,1) | 7 |

21 | The number of line symmetries that the given figure have- – ( A cdot 2 ) B. 4 ( c .3 ) D. | 7 |

22 | The order of rotational symmetry of a ceiling fan with 3 blades is A . 2 B. 3 ( c cdot 4 ) ( D cdot 6 ) | 7 |

23 | If ( boldsymbol{P}=(8,6) ) and ( mathrm{R} ) is the rotation through ( 90^{circ} ) about ( 0, ) then ( R_{-90} O(P) ) is A. (6,-8) () в. (-8,-6) ( c cdot(8,6) ) D. (-8,6) | 7 |

24 | Can you draw a triangle having: no line of symmetry. | 7 |

25 | The number of lines of symmetry for a line segment A. Is infinite B. One c. Two D. None | 7 |

26 | begin{tabular}{|c|} hline \ hline \ hline \ hline \ hline \ hline end{tabular} | 7 |

27 | Statement-1: The point ( A(1,0,7) ) is the mirror image of the point ( B(1,6,3) ) in the line ( frac{x}{1}= ) ( frac{y-1}{2}=frac{z-2}{3} ) Statement-2: The line: ( frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) bisects the line segment joining ( A(1,0,7) ) and ( B(1,6,3) ) A. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement- -1 B. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement- c. Statement-1 is true, Statement-2 is false D. Statement-1 is false, Statement-2 is true | 7 |

28 | Point ( P(6,6) ) lies on the circle with center (2,3) and radius 5 coordinate units. Find the co-ordinates of the image of point ( mathrm{P} ) after the circle is rotated ( 90^{circ} ) clockwise ( ( circlearrowright ) ) about its center. A ( .(2,3) ) B. (3,2) ( c cdot(5,-1) ) ( D cdot(6,0) ) E. (7,3) | 7 |

29 | n the given figure, which of the following is a line of symmetry? A. Line A B. Line B c. Line A and B D. Line | 7 |

30 | What other name can you give to the line symmetry of: an isosceles triangle | 7 |

31 | What is the order of rotational symmetry of a regular pentagon? A . 2 B. 5 c. 10 D. 15 | 7 |

32 | The order of rotational symmetry for the given figure is A. 3 B. 4 ( c cdot 6 ) ( D cdot 12 ) | 7 |

33 | What is the order of rotational symmetry of rectangle? ( A ) B. 2 ( c cdot 3 ) ( D ) | 7 |

34 | The order of rotational symmetry for the given figure is ( A cdot 4 ) B. 3 ( c cdot 2 ) ( D ) | 7 |

35 | The lines of symmetry of a ( -ldots—- ) are the lines joining the mid-points of the opposite sides. A. square B. triangle c. rectangle D. isosceles | 7 |

36 | What is the smallest number of squares that must be added so that the line ( A B ) becomes a line of symmetry? ( A ) B. 2 ( c .5 ) D. | 7 |

37 | Find the coordinates of the foot of perpendicular drawn from the point ( A(-1,8,4) ) to the line joining the points ( B(0,-1,3) ) and ( C(2,-3,-1) . ) Hence, find the image of the point ( A ) in the line ( boldsymbol{B C} ) | 7 |

38 | 8 different shapes are given in the following figure. How many shapes have 0 lines of symmetry? | 7 |

39 | The image of the point (1,6,3) in the line ( frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) has the coordinates A. (1,1,7) в. (0,1,7) c. (1,0,7) D. None of these | 7 |

40 | What is the order of rotational symmetry of the given figure? ( A cdot 6 ) B. 4 ( c cdot 8 ) D. None of these | 7 |

41 | n the given figure, which of the following is a line of symmetry? A. Line A B. Line B c. Line D. Non | 7 |

42 | The number of lines of symmetry in a regular hexagon is A . 4 B. 5 ( c .6 ) D. 7 | 7 |

43 | The lines of symmetry in the double- headed arrow AB are ( A ) B. 1 ( c ) ( D ) | 7 |

44 | Divide the given shape in a Horizontal symmetry (into 2 trapeziums) (iii) into 2 trapeziums | 7 |

45 | Write all the capital letters of the English alphabets which have two lines of symmetry. ( A cdot H, operatorname{land} x ) B. A,C and B c. ( P, Q ) and ( R ) D. s,Y and z | 7 |

46 | ( triangle A B C ) is an isosceles triangle with ( A B=A C . ) Then the line of symmetry for the ( triangle A B C ) will be: This question has multiple correct options A. Perpendicular bisector of ( B C ) B. Angle bisector of ( angle B ) C. Altitude from vertex ( A ) on line ( B C ) D. Median from vertex ( C ) to side ( A B ) | 7 |

47 | The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry is – A. 0 B. ( c cdot 4 ) D. | 7 |

48 | State for ‘T’ true and ‘F’ for false. (i) Number 0 has both rotational and line of Symmetry. (ii) A regular polygon of ( n ) sides has ( 2 n ) lines of symmetry. (iii) A square has four lines of symmetry and rotational symmetry of order 2 (iv) A circle has finite number of lines of symmetry. (i) (ii) (iii) (iv) ( A cdot T F F F ) B. T F T F c. F T F ( T ) D. F T T T | 7 |

49 | Which figure below shows two quadrilaterals related by both rotational symmetry and line symmetry? A. Figure B. Figure i C. Figure iii D. None of these | 7 |

50 | Find a transformation of the polygon that does result in at least one type of symmetry. Draw the image and list the coordinates of the vertices of the larger shape. How do you know the diagram has symmetry? | 7 |

51 | Can you draw a triangle which has no lines of symmetry? Sketch a rough figure. | 7 |

52 | A line ( y=x ) is rotated through ( 60^{circ} ) Find the new angle made by line with ( x ) axis. A . ( 105^{circ} ) B. ( 135^{circ} ) ( mathbf{c} cdot 155^{circ} ) D. ( 120^{circ} ) | 7 |

53 | What is the order of rotational symmetry about the marked point? | 7 |

54 | The diagram shows the outline of a 50 cent coin from Fiji How many lines of symmetry does it | 7 |

55 | The number-of line symmetries that the given square have: ( A ) ( B ) ( c ) ( D ) | 7 |

56 | The number of lines of symmetry in a picture of Taj Mahal is – – A. B. 2 ( c cdot 0 ) ( D ) | 7 |

57 | If a scalene triangle is cut along its line of symmetry, then the number of triangles so formed is A . 1 B. 2 ( c .3 ) D. none of the above | 7 |

58 | Can you draw a triangle which has exactly three lines of symmetry? Sketch a rough figure. | 7 |

59 | How many lines of symmetry are there for an isosceles triangle? A . 1 B. ( c cdot 3 ) ( D ) | 7 |

60 | Name the quadrilaterals which have both line and rotational symmetry of order more than 1 | 7 |

61 | Find the order of rotational symmetry of equilateral triangle. A .2 B. 3 ( c cdot 4 ) D. | 7 |

62 | Draw, wherever possible, a rough sketch of: A triangle with both line and rotational symmetries of order more than 1 | 7 |

63 | What is the order of rotational symmetry about the marked point? | 7 |

64 | The image of the point (3,-1,11) w.r.t the line ( frac{boldsymbol{x}}{mathbf{2}}=frac{boldsymbol{y}-boldsymbol{2}}{boldsymbol{3}}=frac{boldsymbol{z}-boldsymbol{3}}{boldsymbol{4}} ) is | 7 |

65 | Which square must be shaded so that the figure has a line of symmetry? begin{tabular}{|l|l|l|l|} hline & & & \ hline & ( mathbf{R} ) & & \ hline & ( mathbf{P} ) & & ( mathbf{Q} ) \ hline & & & ( mathbf{S} ) \ hline end{tabular} ( A cdot P ) в. ( Q ) ( c . R ) D. | 7 |

66 | The number of rotational symmetry of an equilateral triangle is/are: A . B. ( c cdot 3 ) ( D ) | 7 |

67 | symmetry exists when the figure can be rotated and the image is identical to the original. A. Rotational B. Linear c. Reflection D. Non-linear | 7 |

68 | Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any implication between lines of symmetry and point symmetry? | 7 |

69 | Where will the hand of a clock stop if it: Start at 4 and makes ( frac{3}{4} ) of a revolution, clockwise? | 7 |

70 | What do you face when we make an ( frac{3}{4} ) revolution anti-clockwise from west? | 7 |

71 | topp onwo ( ^{80^{circ}} ) | 7 |

72 | Can you draw a triangle having: three lines of symmetry. | 7 |

73 | Which figure shows the rotation image of pentagon ( A ) after a ( 216^{circ} ) clockwise rotation about its centre? A. Figure iii B. Figure c. Figure iv D. Figure i | 7 |

74 | The number of lines of symmetry for a rectangle is/are A . 1 B. 2 ( c .3 ) ( D ) | 7 |

75 | The reflection of the point ( boldsymbol{P}(1,0,0) ) in the line ( frac{boldsymbol{x}-mathbf{1}}{mathbf{2}}=frac{boldsymbol{y}+mathbf{1}}{mathbf{- 3}}=frac{boldsymbol{z}+mathbf{1 0}}{mathbf{8}} ) is A ( cdot(3,-4,-2) ) B ( cdot(5,-8,-4) ) c. (1,-1,-10) D. (2,-3,8) | 7 |

76 | The diagram shows the outline of a 50 cent coin from Fiji What is its order of rotational symmetry? ( A ) 8. ( c cdot 12 ) D. 15 | 7 |

77 | A ( ——– ) has only one line of symmetry, two sets of equal sides and only one set of matching angles. | 7 |

78 | In the given figure, which of the following is a line of symmetry? A. Line A B. Line B c. Line D. Line A and Line C | 7 |

79 | The projection of the line ( x+y=0 ) ( z=0 ) on the plane ( x-y+z=1 ) is begin{tabular}{l} A ( cdot frac{3 x-1}{3}=frac{3 y+1}{-3}=frac{3 z-1}{-2} ) \ hline end{tabular} B. ( frac{4 x-1}{3}=frac{2 y+1}{-3}=frac{4 z+1}{-6} ) begin{tabular}{l} C. ( frac{3 x-1}{-3}=frac{3 y+1}{3}=frac{3 z-1}{6} ) \ hline end{tabular} D. ( frac{4 x-1}{2}=frac{2 y+1}{1}=frac{4 z+1}{-2} ) | 7 |

80 | The image of the point (1,6,3) in the ( operatorname{line} frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) is A. (1,0,7) в. (1,3,5) c. (2,4,6) D. (-1,-6,-3) | 7 |

81 | The image of the origin in the line joining the points (-9,4,5) and (11,0,-1) is A. (2,4,4) в. (1,2,2) c. (1,2,3) D. (2,2,1) | 7 |

82 | On a squared paper, sketch the following: A triangle with a horizontal line of symmetry but no vertical line of symmetry. | 7 |

83 | Rectangle ABCD is the image of rectangle ABCD after which of the following rotations? A . A ( 90^{circ} ) clockwise rotation about the origin B. A ( 90^{circ} ) clockwise rotation about the point (1,1) C. A ( 90^{circ} ) counterclockwise rotation about the point (1,1) D. A ( 90^{circ} ) clockwise rotation about the point (2,1) | 7 |

84 | A rectangle DEFG is plotted in ( X Y ) plane. The co-ordinates of D , E , F and G ( operatorname{are}(2,2),(9,2),(9,10) ) and (2,10) Find the new co-ordinates of G when DEFG is rotated ( 270^{circ} ) around origin. This question has multiple correct options A ( cdot(-10,2) ) B. (10,-2) c. (10,-1) D. (10,2) | 7 |

85 | What is the order of rotational symmetry of the above pattern? ( A ) ( B ) ( c cdot 12 ) ( D ) | 7 |

86 | What is the order of rotational symmetry of the above pattern? ( A cdot 3 ) ( B ) ( c cdot 6 ) D. 12 | 7 |

87 | An equilateral triangle whose each side is ( 4.5 mathrm{cm} . ) How many lines of symmetry does it has???????? ( A cdot 3 ) B. 2 ( c ) D. infinite | 7 |

88 | Which of the following is symmetrical about its diagonals? A. Square B. Rectangle c. Parallelogram D. None of these | 7 |

89 | A line ( y=x ) is rotated through ( 45^{circ} ) Find the new angle made by line with ( x ) axis. A ( cdot 90^{circ} ) B. ( 80^{circ} ) ( c .75^{circ} ) D. None of these | 7 |

90 | The number of lines of symmetry that the given square has is ( A cdot 4 ) B. 2 ( c cdot 3 ) D. | 7 |

91 | A protractor has – symmetry. A . B. 2 ( c .3 ) ( D ) | 7 |

92 | How many of the alphabets have more than 1 line of symmetry? [ A B C D E F G H I J K L M N O ] | 7 |

93 | How many lines of symmetry are there for an equilateral triangle. | 7 |

94 | John notices that a standard piece of paper is a rectangle, how many lines of symmetry does it have? ( A ) B. 2 ( c cdot 3 ) D. 4 | 7 |

95 | A figure has a rotational symmetry of order more than 1 , the angle of rotation can be A ( cdot 21^{circ} ) B . ( 22^{circ} ) ( c cdot 23^{circ} ) D. ( 24^{circ} ) | 7 |

96 | The number of lines of symmetry in a regular pentagon is A . 3 B. 4 ( c .5 ) ( D ) | 7 |

97 | A rectangle DEFG is plotted in ( X Y ) plane. The co-ordinates of D , E , F and G ( operatorname{are}(2,2),(9,2),(9,10) ) and (2,10) Find the new co-ordinates of D when DEFG is rotated ( 270^{circ} ) around origin. A ( cdot(-2,-2) ) в. (2,-2) c. (2,4) (年. ( (2,4)) ) D. (-2,4) | 7 |

98 | When a right triangle of area 3 is rotated ( 360^{circ} ) about its shorter leg, the solid that results has a volume of 30 Calculate the volume of the solid if the same right triangle is rotated about its longer leg. A . 0.99 B. 7.90 c. 8.88 D. 31.42 E . 41.12 | 7 |

99 | Draw neat diagrams showing the line (or lines) of symmetry and give the specific name to the quadrilateral having: only one line of symmetry. How many quadrilaterals are there? | 7 |

100 | Which of the squares must be shaded so that the dotted line AB becomes the line of symmetry? ( A ) B. ( I I ) c. ( I I I ) D. ( I V ) | 7 |

101 | How many minimum squares must be shaded to make the given figure symmetric ? ( A ) B. ( c ) ( D ) | 7 |

102 | This star is made up of equilateral triangles: What is the order of rotational symmetry of the star? ( A ) ( B ) ( c ) D. 12 | 7 |

103 | On squared paper copy the triangle in the following figure. In a given case draw the line (s) of symmetry if any identify the type of the triangle. | 7 |

104 | Write the number of lines of symmetry in each letter ‘SYMMETRY’. | 7 |

105 | The number of lines of symmetry in a square is A . 4 B. 3 ( c cdot 2 ) D. Infinite | 7 |

106 | What is the order of rotational symmetry and angle of rotation symmetry for this design? A ( cdot 4 ; 90^{circ} ) B. ( 6 ; 120^{circ} ) c. ( 8: 60^{circ} ) D . ( 8 ; 45^{circ} ) | 7 |

107 | Fill in the blanks. Rotation turns an object about a ( P ) point. The fixed point is the centre of ( underline{Q} ) The angle by which the object rotates is the ( R ) Then, P Q R is: A. fixed rotation angle of rotation B. variable rotation central angle c. fixed angle of rotation rotation D. variable rotation angle of rotation | 7 |

108 | What is the order of rotational symmetry of this star? ( A ) 3.4 ( c ) ( D ) | 7 |

109 | Assertion The point ( boldsymbol{A}(mathbf{1}, mathbf{0}, mathbf{7}) ) is the mirror image of the point ( B(1,6,3) ) in the line ( : frac{x}{1}= ) ( frac{boldsymbol{y}-mathbf{1}}{mathbf{2}}=frac{boldsymbol{z}-mathbf{2}}{mathbf{3}} ) Reason The line ( frac{x}{1}=frac{y-1}{2}=frac{z-2}{3} ) bisects the line segment joining ( boldsymbol{A}(mathbf{1}, mathbf{0}, mathbf{7}) ) and ( boldsymbol{B}(mathbf{1}, mathbf{6}, mathbf{3}) ) A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect | 7 |

110 | A rectangle has A. Two lines of symmetry B. Four lines of symmetry C. Three lines of symmetry D. None of these | 7 |

111 | How many lines of symmetry does the figure have? A. 0 B. 1 ( c cdot 2 ) ( D ) | 7 |

112 | After rotating by ( 60^{circ} ) about a centre, a figure looks exactly the same as at its original position. At what other angle will this happen for the figure? ( mathbf{A} cdot 120^{circ} ) B. 100 ( c cdot 150 ) D. ( 90^{circ} ) | 7 |

113 | A rectangle has A. one line of symmetry B. two lines of symmetry C. three lines of symmetry D. None of these | 7 |

114 | This polygon is one-half of a shape. Use a vertical line through 5 on the ( x ) -axis as a line of symmetry to complete the shape by drawing its other half. Write the coordinates of the larger shape formed by PQRS and its image. | 7 |

115 | ( = ) | 7 |

116 | John notices that a standard piece of paper is a rectangle ( ldots ) how many lines of symmetry does it have? A . 1 B . 2 ( c .3 ) D. 4 | 7 |

117 | If a rectangle has more than two lines of symmetry,then it must be a square. A. True B. False | 7 |

118 | How many lines of symmetry are in this isosceles triangle? ( A ) B. 2 ( c cdot 3 ) ( D ) | 7 |

119 | The angle of rotation symmetry for a shape is ( 60 . ) What is the order of rotational symmetry? ( A cdot 6 ) B. 4 ( c cdot 3 ) D. 8 | 7 |

120 | Find the image of the point (2,-1,5) in the line ( vec{r}=(11 hat{i}-2 hat{j}-8 hat{k})+ ) ( lambda(10 hat{i}-4 hat{j}-1 hat{1} k) ) | 7 |

121 | Let, coordinates of the two points ( A & B ) be (1,2) and ( (7,5), ) respectively. The line ( A B ) is rotated through ( 45^{circ} ) in anticlockwise direction about the point of trisection of ( mathrm{AB} ) which is nearer to B. The equation of the line in the new position is A. ( 2 x-y-6=0 ) в. ( x-y-1=0 ) c. ( 3 x-y-11=0 ) D. none of these | 7 |

122 | Give the order the rotational symmetry for each figure: | 7 |

123 | A rectangle DEFG is plotted in ( X Y ) plane. The co-ordinates of D , E , F and G ( operatorname{are}(2,2),(9,2),(9,10) ) and (2,10) Find the new co-ordinates of F when DEFG is rotated ( 270^{circ} ) around origin. This question has multiple correct options A ( cdot(-10,9) ) B. (-10,-9) c. (10,9) D. (10,-9) | 7 |

124 | Find the order of rotational symmetry Refer above image. | 7 |

125 | How many of the following letters have rotational symmetry of order more than 1? ( mathrm{R}, mathrm{B}, mathrm{F}, mathrm{H}, mathrm{O}, mathrm{P}, mathrm{S}, mathrm{W}, mathrm{X}, mathrm{Z}, mathrm{N} ) A .4 B. 9 ( c .5 ) ( D ) | 7 |

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