Class 7 Maths Notes for Symmetry

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CLASS 7
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SYMMETRY
IMPORTANT CONCEPTS

 Symmetry is a geometrical concept that is found in most cases including nature.
 Any geometric shape can be said to be symmetric or asymmetric
 A shape is said to be symmetric if there exists an imaginary line passing through that
divides the shape into halves and that these halves overlap each other completely.
 In other words, fold the shape about the imaginary line to check if the two halves
completely overlap each other or not. If they overlap each other completely the shape is
symmetric, if not, then it is asymmetric.
 The imaginary line is called as the line of symmetry.
 The symmetry observed in the above example is called as a line symmetry or bilateral
symmetry.

Lines of Symmetry for Regular Polygons

 Regular polygons are closed shapes that have equal sides and equal angles.
 Such polygons have multiple lines of symmetry.
Some regular polygons with their line of symmetry are shown below:

Rotational Symmetry

 There exists another concept of symmetry that does not involve folding the figure to
check if they coincide.
 Rotational symmetry is one where when a figure is rotated about a centre point, the figure
looks exactly the same before rotation.
 The particular centre for which rotational symmetry is observed is called the centre of
rotation.
 The angle of turning during rotation is called angle of rotation.
 The number of positions in which a figure can be rotated and still appears exactly like it
did before the rotation is called order of symmetry.

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SOME EXAMPLES(With Solutions)
MCQs
Q1. The angle of rotation of an isosceles triangle is
(a) 120° (b) 270 (c) 180° (d) 360° Sol: (c)
180°
Q2 The order of rotational symmetry of the following figure is:

(a) 1 (b) 2 (c) 3 d) 4 Sol: b) 2
Q3 . Find the number of lines of symmetry of an Equilateral triangle?
(a) 1 (b) 2 (c) 3 (d) 4 Sol : c) 3
Q4 Which of the followings has both horizontal as well as vertical line of symmetry
(a) S (b) A (c) U (d) H Sol : d)
H

Case based study Qyestion
The Universal Recycling symbol is rendered with a black outline and green fill and is
internationally recognized for recycling activity. Both filled and outline versions are in use. To
raise awareness of environmental issues, a contest on designing the Universal designing symbol
was won by a 23- year old university student named Gary Anderson. The logo is usually
displayed with the arrows circulating clockwise. The triangle is made up of three arrows drawn
as a continuous loop.

Question 1.1: The number of times this logo coincides one full rotation in clockwise direction
is:
i. Two times ii. Three times iii. Four times iv. None of the
above.
Question 1.2: The direction of rotation of logo is:
(i) clockwise (ii) anticlockwise
Question 1.3: Does the logo show rotational symmetry ?
Solution: 1.1 Three times
1.2 clockwise
1.3 yes
SHORT ANSWER TYPE QUESTIONS
Q1 . Give an example of a geometrical figure which has neither a line of symmetry nor a
rotational symmetry.
Solution: A scalene triangle has neither a line of symmetry nor a rotational symmetry.

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Q2 . Give an example of a geometrical figure which has neither a line of symmetry nor a
rotational symmetry.
Solution: A semicircle and an isosceles triangle have a line of symmetry but do not have
rotational symmetry.

Q3 Give an example of a letter of the English alphabet which has
(i) No line of symmetry
(ii) Rotational symmetry of order 2.
Solution:
(i) The letter of the English alphabet which has no line of symmetry is Z.
(ii) The letter of the English alphabet which has rotational symmetry of order 2 is N.

LONG ANSWER TYPE QUESTIONS
Q1 Fill in the blanks.

Shape Centre of rotation Order of rotation Angle of rotation

Semi-circle

Circle

Regular hexagon

Equilateral triangle

Rhombus

Rectangle

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Solution :
Shape Centre of rotation Order of Angle of rotation
rotation

Semi-circle Mid-pointer of diameter is 1 360 degrees represent the angle of
the centre of rotation. rotation.

Circle Centre depicts the centre of infinite Every angle represents the angle
rotation. of rotation.

Regular Intersecting point of 6 60 degrees represent the angle of
hexagon diagonals is the centre of rotation.
rotation.

Equilateral Intersecting points of media 3 120 degrees represent the angle of
triangle is the centre of rotation rotation.

Rhombus Intersecting point of 2 180 degrees represent the angle of
diagonals is the centre of rotation.
rotation.

Rectangle Intersecting point of 2 180 degrees represent the angle of
diagonals is the centre of rotation.
rotation.

Q2 Fill in the blanks

 The fixed point around which the rotation turns the object is known as ____
 ____________ is the angle at which the object rotates.
 A half-turn refers to rotation by _________
 The rotation could be either ______ or _________
 In ____________ , complete rotation of 360 degrees, the number of times the object
looks exactly the same.
Solution 1. Centre of rotation
2. angle of rotation
3. 180 degrees
4. clockwise or anticlockwise 5. order of rotational symmetry

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QUESTION FOPR PRACTICE
MCQs
Q1 The order of rotational symmetry of a circle is
(a) 1 (b) 4 (c) 2 (d) infinite
Q2. How many lines of symmetry are there in the following figure?

(a) 1(b) 2 (c) 3 (d) 4
Q3 How many lines of symmetry are there in a scalene triangle?
(a) 1(b) 0 (c) 2 (d) 4
Q4. The order of the rotational symmetry of the following figure about the point marked x is

(a) 1 (b) 2 c)3 d) 4
Q5. The order of rotational symmetry of a circle is:
(a) 1(b) 4 (c) 2 (d) infinite
Q6. The rotational symmetry of order

a)1 b) 2 c) 3 d) 4
Q7. A figure which can be rotated into itself is said to have ………………….. symmetry.
Q8. The number of times a figure fits into itself in one complete rotation is called the order of
………………….. symmetry.
Q9. Rotating a figure through 90° clockwise is the same as rotating it anti-clock wise through
…………………. [270°/180°]
Q10. Which of the following has only one line of symmetry?
(a) A rectangle(b) A square (c) A semi circle (d) An equilateral triangle

SHORT ANSWER TYPE QUESTIONS
Q1. Give an example of the English letter or alphabet which has reflectional symmetry about a
vertical mirror.
Q2 Draw and name the two figures which have both line symmetry and rotational symmetry.
Q3. Name a triangle which has only one line of symmetry and has no rotational symmetry of
order of more than 1.
Q4. Answer the following question in yes or no.

Can we have a rotational symmetry of order more than 1 when 45 degrees is the angle of
rotation?

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Q5. Can we have a rotational symmetry of order more than 1 whose angle of rotation is 17
degrees?

Q6. Give two examples of figures having both line and rotational symmetry.

Q7. What is the name of the solid which has one circular face , one curved surface and one
vertex.

Q8. When a torch is pointed towards one of the vertical edge of the cube, what shadow will you
get?

Q9. How many faces , edges and vertices does a square pyramid has?

Q10. Each of the letter H,N,S,Z has rotational symmetry of which order?

LONG ANSWER TYPE QUESTIONS
Q1.Match the following:

Column A Column B
(1) A rectangle has a rotational symmetry of
(a) Infinite
order………..
(2) An equilateral triangle has ……….. lines of symmetry (b) 6
(3) A circle has …………. lines of symmetry. (c) 1
(4) The letter ―A‖ has rotational symmetry of
(d) 3
order………….
(5) The number of lines of symmetry of a regular hexagon
(e) 2
is ……..

Q2. How many lines of symmetry do the following have:
(a) a parallelogram.
(b) an equilateral triangle.
(c) a right angle with equal legs.
(d) an angle with equal arms.

Q3.After rotating by 600 about a centre,a figure looks exactly the same as its original position. At
what other angles will this happen for the figure?
Q4) Can you now tell the order of the rotational symmetry for an equilateral triangle?

(b) How many positions are there at which the triangle looks exactly the same, when rotated
about its centre by 120°?

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Q5) Which of the following shapes have rotational symmetry about the marked point.

Q6.) Give the order of the rotational symmetry of the given figures about the point marked x

CASE BASED STUDY QUESTIONS
Q1.The left side of an object appears to be the right side in the mirror. When the driver of the
front vehicle sees the word ―Ambulance‖ in the rear view mirror, he can see the inverted image
of the word and read it correctly giving way to the Ambulance.
Question 1.1: Why are the letters of Ambulance reversed?
Question 1.2: Find out the alphabet which was not changed if we take horizontal and vertical
image both.
Question 1.3: Find out four alphabets which remains unchanged when we take their vertical
mirror image.

Q2. Mohan writes ―W‖on a tracing paper and draws a line vertically on it at the centre as shown
in the following figure.He then folds the paper along the line and gets two parts of alphabet W.

Question 2.1: Do the two parts coincide with each other?
Question 2.2: What will happen if he draws a line horizontally on it at the centre and fold the
paper along the horizontal line?
Question 2.3: Answer the following questions:-
Observation Say Yes/ No (a) Does W have horizontal line of symmetry? Yes/No
(b) Does W have vertical line of symmetry? Yes/No
Question 2.4: Find out the letters given in the above image having vertical line of symmetry.

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ANSWERS FOR PRACTICE QUESTIONS
MCQS
Ans1)infinite Ans2) 1 Ans3 ) 0 Ans4) 3
Ans 5) infinite Ans6) 2 Ans 7) point Ans 8 ) Rotational
0
Ans9) 270 Ans 10) semicircle

SHORT ANSWER TYPE QUESTIONS
Q1. A, H, I, M, O, U, V, W, X, YQ2 : Equilateral triangle Ans 3) an isosceles triangle.
Ans4) yesAns5) noAns6) regular hexagon and equilateral triangle
Ans7) coneAns8) rectangle but not a squareAns9) F-5, E-8, V-5
Ans10) 2
LONG ANSWER TYPE QUESTIONS
Ans1) 1e , 2d, 3a, 4c, 5bAns2) a-0, b-3, c-1,d- 2
Ans3) 1200, 1800, 2400, 3000, 3600Ans4) a-3, b-4Ans5) (i)Ans6) (i)4 (ii)3 (iii)2
CASE BASED STUDY QUESTIONS
Ans1) 1.1- reversed so that driver sees the right way around in the rear view mirror
1.2- O
1.3- A,H,I,M
Ans2) 2.1- yes 2.2- does not coincide 2.3- no , yes 2.4 I, H
QUESTION PAPER ( OF 20 MARKS)
Q1. Find the number of lines of symmetry of an Equilateral triangle? (2)
Q2 Find out the angle of rotation of an isosceles triangle . (2)
Q3 Give three example of a geometrical figure which has neither a line of symmetry nor a
rotational symmetry. (3)
Q4 . How many lines of symmetry do the following have: (3)
(a) a parallelogram.
(b) an equilateral triangle.
(c) a right angle with equal legs.
Q5 How many faces , edges and vertices does a square pyramid has? (3)
Q6 Give an example of a letter of the English alphabet which has (3)
(i) No line of symmetry
(ii) Rotational symmetry of order 2.
Q7 . Each of the letter H,N,S,Z has rotational symmetry of which order?
Q8 Give an example of a letter of the English alphabet which has (4)
(i) No line of symmetry(ii) Rotational symmetry of order 2.
Question paper of 30 marks
Q1. Name a triangle which has only one line of symmetry and has no rotational symmetry of
order of more than 1 (2)
Q2 Draw and name the two figures which have both line symmetry and rotational symmetry.
(2)

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Q3 Draw a figure having an infinite number of lines of symmetry.
(2)
Q4 Give three examples of shapes with no line of symmetry. (2)

Q5 What other name can you give to the line of symmetry of (3)

(a) an isosceles triangle? (b)a circle (c) equilateral triangle

Q6 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 (3)

Q7 State the number of lines of symmetry for the following figures: (4)

(a) An equilateral triangle (b) An isosceles triangle (c) A scalene triangle (d) square
Q8 fill in the blanks: (4)
 The fixed point around which the rotation turns the object is known as ____
 ____________ is the angle at which the object rotates.
 A half-turn refers to rotation by _________
 The rotation could be either ______ or _________

Q9 State true or false: (4)
(i) When an object rotates, its shape changes.
(ii) if a shape possess rotational symmetry, it will surely have line of symmetry.
(iii) We can not have a rotational symmetry of order more than 1 whose angle of rotation is 23°
(iv) A pentagon which has more than one line of symmetry must be regular.
Q10 (4)
Shape Centre of rotation Order of rotation Angle of rotation

Semi-circle

Circle

Regular hexagon

Equilateral triangle

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