Haryana Board Class 7 Maths Solutions For Chapter 12 Symmetry

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Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Key Concepts

  1. Introduction:
    Symmetry is an important geometrical concept, commonly exhibited in nature and is used almost in every field of activity. Artists, professionals, designers of clothing or jewellery, car manufacturers, architects, and many others make use of the idea of symmetry. The beehives, the flowers, the tree leaves, religious- symbols, rugs, and handkerchiefs – everywhere you. find symmetrical designs.
  2. Line symmetry: A figure has line symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide.
  3. Lines of symmetry for regular polygons:
    A polygon is said to be regular if all its sides are of equal length and all its angles are of equal measure. The polygon is a closed figure made, of several line segments

    1. The polygon made up of the least number of line segments is the triangle. An equilateral triangle is a regular polygon of three sides. Each of its sides has same length and each of its angles measures 60°.
    2. A square is a regular polygon of four sides. Each of its sides has’same length and each of its angles measure 90°. Its diagonals bisect each other perpendicularly.
    3. If a pentagon is regular, its sides should have equal length.
    4. A regular hexagon has all its sides equal and each of its angles measures 120°. Regular polygons are symmetrical figures. Each regular polygon has many lines of symmetry as it has several sides.
      Equilateral triangle – 3 lines of symmetry
      Square- 4 lines of symmetry
      Regular pentagon – 5 lines of symmetry
      Regular hexagon – – 6 lines of symmetry
  4. Symmetry and mirror reflection:
    The concept of linesymmetry is closely related to mirror reflection. A shape, has line symmetry. when one half of it is the mirror image of the other half. A mirror, line, thus, helps to visualized line of symmetry.
  5. Perfect symmetry: The circleIs the most symmetrical figure because it can be rotated around its centre through any angle and at the same time it unlimited number of lines of symmetry.
  6. Angle of rotational symmetry: The minimum angle of rotation of a figure to get exactly the same figure as original is called the “Angle of rotational symmetry. ”
    • The angle of rotation of symmetry of a square is 90°.
    • The angle of rotation of symmetry of a parallelogram is 180°.
    • The angle of rotation of symmetry of a circle is 0 to 360°.
  7. Order of rotational symmetry: The number of times a figure rotated through its angle of rotational symmetry before it comes to original position is called the “Order of rotational symmetry”.
    • The order of rotational symmetry of a square is 4
    • The order of rotational symmetry of an equilateral triangle is 3.
    • The formula for the order of rotational symmetry of a regular polygon \( =\frac{360^{\circ}}{\text { angle of symmetry }} \)
  8. Clearly all figures have rotational symmetry of order 1. So, we say that an object has rotational symmetry, only when the order of symmetry is more than 1.
  9. Some figures only have line symmetry,and some have only rotational symmetry and some figures have both. Squares, equilateral triangles, and circles have both the line and rotational symmetry.

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Exercise 12 .1

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

 

Each figure is symmetrical and is shown by dotted lines.

Each figure is symmetrical and is shown by dotted lines

HBSE Class 7 Symmetry Solutions

2. Given the line(s) of symmetry, find the other hole(s):

Given the line(s) of symmetry, find the other hole

Solution:

Given the line(s) ofsymmetry, find the other hole 1

Haryana Board Class 7 Maths Symmetry solutions

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?
In the following figures, the mirror line (i.e. the line of symmetry) is given as a
Solution:
In the following figures, the mirror line (i.e. the line of symmetry) is given as a 1
4. The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
The following figures have more than one line of 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
Key Questions in Symmetry for Class 7 HBSE
Solution:
Identify multiple lines of symmetry, if any, in each of the following figures 1
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?
Copy the figure given here
Solution:
Copy the figure given here 1
Yes, there is one more way to do. That is, on taking second diagonal as line of symmetry. Yes, the figure will be symmetric about both the diagonals.
Copy the figure given here 2
HBSE 7th Class Rotational Symmetry Explained
6. Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Copy the diagram and complete each shape to be symmetric about the mirror line
Solution:
Copy the diagram and complete each shape to be symmetric about the mirror line 1
7. State the number of lines of symmetry for the following figures:
  1. An equilateral triangle – Three
  2. An isosceles triangle – One
  3. A scalene triangle – None
  4. A square – Four
  5. A rectangle – Two
  6. A rhombus – Four
  7. A parallelogram -None
  8. A quadrilateral -None
  9. A regular hexagon -Six
  10. A circle – Unlimited

How to find lines of symmetry Class 7 HBSE

8. What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about.
  1. a vertical mirror
  2. a horizontal mirror
  3. both horizontal and vertical mirrors
Solution:
  1. About vertical mirror: A, H, I, M, O, T, U, V, W, X, Y
  2. bout horizontal mirror: B, C, D, E, H, I, K, O, X
  3. About both horizontal and vertical mirrors: H, I, O, X
9. Give three examples of shapes with no line of symmetry.
Solution:
  1. A scalene triangle
  2. A trapezium
  3. The letter G

Sample Problems Symmetry Haryana Board Class 7

10. What other name can you give to the line of symmetry of
  1. an isosceles triangle ?
  2. a circle?
Solution:
Other name to the line of symmetry of
1) an isosceles triangle is median
2) a circle is diameter.

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Solutions

1.
1) Can you now tell the order of the rotational symmetry for an equilateral triangle?
Can you now tell the order of the rotational symmetry for an equilateral triangle
Solution: The order of the rotational symmetry for an equilateral triangle is 3.
2) How many positions are there at which the triangle looks exactly the same, when rotated about its centre by 120°?
Solution:
There are two positions at which the triangle looks exactly the same when rotated about its centre by 120″.
2. Which of the following shapes have rotational symmetry about the marked point?
Solution:
Which of the following shapes have rotational symmetry about the marked point
Shapes having rotational symmetry about the marked point are (1), (2), (3) and (4).
Give the order of the rotational symmetry of the given figures about the point marked x.
Give the order of the rotational symmetry of the given figures about the point marked x
Solution:
Order of the rotational symmetry of the given figures are:
(1) Four (2) Three (3) Four
Note: In a complete turn (of 360°) the number of times an object looks exactly the same is called the order of rotational symmetry.
The order of symmetry of a square is 4 For equilateral triangle it is 3.

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Exercise-12.2

1. Which of the following figures have rotational symmetry of order more than 1:
Which of the following figures have rotational symmetry of order more than1 q
Solution: All figures have rotational symmetry of order more than 1
Lines of Symmetry Class 7 Haryana Board
2. Given the order of rotational symmetry for each figure.
Which of the following figures have rotational symmetry of order more than1
Solution:
(a) 2 (b) 2 (c) 3 (d) 4 (e) 4 (f) 5 (g) 6 (h) 3
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

Solution:

By attempting to think on such lines, you will be able to fill in the following table solution

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Exercise-12.3

1. Name any two figures that have both line symmetry and rotational symmetry.
Solution:
The two figures that have both line symmetry and rotational symmetry are:
  1. Equilateral triangle and
  2. Circle.
2. Draw, wherever possible, a rough sketch of
  1. a triangle with both line and rotational symmetries of order more than 1.
  2. a triangle with only line symmetry and no rotational symmetry of order more than 1.
  3. a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
  4. a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Solution:
  1. A triangle with both line symmetry and rotational symmetry of order more than 1 is an equilateral triangle.
    equilateral triangle
  2. A triangle with only line symmetry and no rotational symmetry of order more than 1 is an isosceles triangle
    isosceles triangle
  3. A quadrilateral with a rotational symmetry of order more than1 but not a line symmetry is a parallelogram.
    parallelogram
  4. A quadrilateral with a line symmetry but not a rotational symmetry of order more than 1 is an isosceles trapezium.
    isosceles trapezium
HBSE Class 7 Maths Chapter 12 Guide
3. If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Solution:
Yes, a figure that has two or more lines of symmetry have a rotational symmetry of order more than 1.
4. Fill in the blanks:
Fill in the blanks 4
Solution:
Fill in the blanks 4 Answer

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Fill in the blanks:

5. Name the quadrilaterals which have both line and rotational symmetry Of order more than 1.
Solution:
Square, rectangle, and rhombus.
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:
The other angles are 120°, 180°, 240°,300° and 360°.
7. Can we have a rotational symmetry of order more than 1 whose angle of rotation is
  1. 45° ?
  2. 17° ?
Solution:
  1. Yes
  2. No

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Very Short Answer Questions

1. What is meant by’Line Symmetry’?
Solution:
A figure has line symmetry if there is a line about which the figure may be folded so that the two parts of the figure will coincide.
Important Concepts Symmetry Class 7 HBSE
2. Write the number of lines of symmetry for (1) Regular hexagon (2) Square (3) Rectangle.
Solution:
  1. Regular hexagon –   6
  2. Square                 –   4
  3. Rectangle             –   2
3. Write
  1. Centre of rotation
  2. Angle of rotation
Solution:
  1. Rotation turns an object about a fixed point. This fixed point is called the ‘Centre of rotation’.
  2. The angle by which the object rotates is called the’Angle of rotation’.

Examples of rotational symmetry Class 7 HBSE

4. The order of symmetry for
  1. a square
  2. an equilateral triangle.
Solution:
  1. The order of symmetry for a square is 4
  2. The order of symmetry for an equilateral triangle is 3.
5. Name a few things in nature, that are symmetric.
Solution:
Leaf, Butterfly, A person’s face, Fish etc.,
6. Name 5 man-made things that are symmetric.
Solution:
Plank, paper, spectacles, blade, clock without hands, ladder.
7. What is the angle of rotational symmetry of a square?
Solution:
The angle of rotational symmetry of a square is 90°
8. What is the angle of rotational symmetry of a parallelogram?
Solution:
The angle of rotational symmetry of a parallelogram is 180°
9. What is the angle of rotational symmetry of a circle?
Solution: The angle of rotational symmetry of a circle is 0° to 360°
10. Draw any three shapes based on below sentences:
1) No line of symmetry
Solution:
No line of symmetry
2) One line of symmetry
One line of symmetry
Solution:
3) Two lines of symmetry
Two lines of symmetry
Solution:
4) Three lines of symmetry
Solution:
Three lines of symmetry
11. Find whether the following letters of the English alphabet have rotational symmetry or not. If yes, find the point of rotational symmetry (approximately), and also order of rotational symmetry.
Find whether the following letters of the English alphabet have rotational symmetry or not
Solution:
Find whether the following letters of the English alphabet have rotational symmetry or not solution
The letters of the english alphabet that have rotational symmetry are H, S, Z, O.
Order of rotational symmetry
12. Identify which of the english alphabet have point symmetry in the following:
Identify which of the english alphabet have point symmetry in the following 2
Solution:
H and S have point symmetry. Because
1) Every part of the letter has a matching part which are at the same distance from the central point.
Identify which of the english alphabet have point symmetry in the following
2) The part of the alphabet and its. matching part are in the opposite direction.
Identify which of the english alphabet have point symmetry in the following 1
Symmetry Class 7 HBSE important questions
13. Drawsome natural objects which have at least one line of symmetry.
Solution:
Draw some natural objects which have at least one line of symmetry leaf
Draw some natural objects which have at least one line of symmetry moon,lotus,lady bug

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Long Answer Questions

14. Which of the following shapes have line symmetry? Which have rotational symmetry?
1)
Which of the following shapes have line symmetry Which have rotational symmetry
Solution:
  1. It has no line of symmetry.
  2. It has rotational symmetry.
2)
Which of the following shapes have line symmetry Which have rotational symmetry 2
Solution:
  1. It has lines of symmetry.
  2. It has no rotational symmetry.
3)
Which of the following shapes have line symmetry Which have rotational symmetry 3
Solution:
It has 2 lines of symmetry and rotational symmetry.
4)
Which of the following shapes have line symmetry Which have rotational symmetry 4
Solution:
It has 4 lines of symmetry and rotational symmetry.
15. Draw lines of symmetry for the following figures. Identify which of them have point symmetry. Is there any relation between lines of symmetry and point symmetry?
Solution:
Draw lines ofsymmetryfor the following figures solution
Here(1),(2),(3), and(4) figures have point symmetry.
Practice Problems Symmetry Class 7 Haryana Board
16. Cut the capital letters of English and paste them in your notebook. Draw possible number of lines of symmetry for each of the letter
Solution:
Draw possible number of lines of symmetry for each of the letter
1) How many letters have no line of symmetry? What are they?
Solution:
10 letters have no line of symmetry. They are FG J LNPQ RS Z.
2) How many letters have one line of symmetry? What are they?
Solution:
12 letters have one line of symmetry. They are A, C, D, E, I, K, M, T, U, V, W, Y.
3) How many letters have two lines of symmetry? What are they?
Solution:
2 letters have two lines of symmetry. They are H, and X.
4) How many letters have more than two lines of symmetry? What are they?
Solution:
Only one letter have more than two lines of symmetry: ‘O’.
5) Which of them have rotational symmetry? What are they?
Solution:
4 letters have rotational symmetry. They are H, O, S, and Z.
6) Which of them have point symmetry? What are they?
Solution:
7 letters have point symmetry. They are H, I, N, O, S, X and Z.
17. State the number of lines of symmetry for the following figures and draw them.
Solution:

 

1).  An equilateral triangle:

An equilateral triangle has 3 lines of symmetry.

An equilateral triangle

Reflection symmetry examples Class 7 Haryana Board

2). An isosceles triangle:

An isosceles triangle has only one line of symmetry.

An isosceles triangle

3). A scalene triangle:

A scalene triangle has no line of symmetry.

A scalene triangle

 

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry

Choose the correct answers:

1. A regular pentagon has lines of symmetry.
  1. 5
  2. 3
  3. 2
  4. 1
Answer: 1
2. What is the order of rotational symmetry of a square ?
  1. 4
  2. 3
  3. 6
  4. 5
Answer: 1
3. Which of the following shapes has horizontal line of symmetry?
Which of the following shapes has horizontal line of symmetry
  1. 1
  2. 2
  3. 3
  4. 4
Answer: 4
4. Which of the following is not symmetric?
  1. C
  2. L
  3. B
  4. D
Answer: 2
5. Which of the following has line of symmetry?
  1. A scalene triangle
  2. Line segment
  3. Trapezium
  4. The letter G
Answer: 2
6. Which of the following is not matched correctly? figure  order

 

Which of the following is not matched correctly

Answer: 2
7. Which of the following is odd one according to order?
  1. Rhombus
  2. Rectangle
  3. Parallelogram.
  4. Square
Answer: 4
8. Among the following which has rotational symmetry but no line of symmetry
  1. Isosceles triangle
  2. Parallelogram
  3. Circle
  4. Rhombus
Answer: 2
9. Which of the following has both line and rotational symmetry?
  1. Isosceles triangle
  2. Scalene triangle
  3. Square
  4. Parallelogram
Answer: 3
10. What is the other name for a line of symmetry of a circle?
  1. Radius
  2. Diameter
  3. Sector
  4. Arc
Answer: 2
11. Which of the following is true?
  1. A rhombus has four lines of symmetry
  2. A square has four lines of symmetry
  3. A circle has four lines of symmetry
  4. An equilateral triangle has two lines of symmetry
Answer: 2
12. What is the other name given to the line of symmetry of isosceles triangle?
  1. Median
  2. Diameter
  3. Perpendicular
  4. Radius
Answer: 1
13. Which of the letters have both lines of symmetry?
Answer: 1
14. What is the angle of rotation of B> Q equilateral triangle ?
  1. 180°
  2. 90°
  3. 120°
  4. 360°
Answer: 3
15. Statement p: The maximum angle of rotation of a figure to get exactly the same figures as original is called angle of rotational symmetry
Statement q: There is no angle of rotation for quadrilateral.
  1. Both p and q are true
  2. Both p and q are false
  3. p is false q is true
  4. p is true q is false
Answer: 3
16. How many symmetrical axes are there for a round clock?
  1. 3
  2. 4
  3. 5
  4. infinite
Answer: 4
17. Which of the following has one axis of symmetry?
  1. O
  2. B
  3. X
  4. H
Answer: 2
18. The number of axis of symmetry of an equilateral triangle
  1. 1
  2. 2
  3. 3
  4. 4
Answer: 3
19. Find the odd one out

 

Find the odd one out

Answer: 1
20. What is the mirror image of ‘D’…..

 

What is the mirror image of'D'

Answer: 2
21. What is the order of
What is the order of
  1. 0
  2. 2
  3. 3
  4. 4
Answer: 3
22. Identify the number of lines of symmetry for the given figure
Identify the number of lines of symmetry for the given figure
  1. 1
  2. 2
  3. 3
  4. 4
Answer: 2
23. Which of the following has only one line of symmetry?
Which of the following has only one line of symmetry
  1. 1
  2. 2
  3. 3
  4. 4
Answer: 4
24. Number of lines of symmetry for an equilateral triangle are
  1. 3
  2. 1
  3. 2
  4. 4
Answer: 1
25. Number of lines of symmetry for an isosceles triangle are
  1. 1
  2. 2
  3. 3
  4. 4
Answer: 1
26. Number of lines of symmetry for a circle is
  1. 1
  2. 2
  3. 5
  4. infinite
Answer: 4
27. Number of lines of symmetry for a regular pentagon
  1. 6
  2. 4
  3. 5
  4. 3
Answer: 3
28. A quarter – turn means rotation by
  1. 360°
  2. 270°
  3. 180°
  4. 90°
Answer: 4

Haryana Board Class 7 Maths Solutions For  Chapter 12 Symmetry Fill in the blanks:

29. A regular hexagon has all its sides equal and each of its angle measures………..
Answer: 120°
30. A full-turn means a rotation of…..
Answer: 360°
31. Number of lines of symmetry for the letter E……..
Answer: 1
32.. Order of rotational symmetry for the letter Z ……………
Answer: 2
33. The centre of rotation is the….. of the square.
Answer: centre
34. Number of lines of symmetry of an equilateral triangle……
Answer: 3
35. Number of lines of symmetry of an isosceles triangle…….
Answer: 1
36. Number of lines of symmetry of scalene triangle……
Answer: 0
37. A polygon with all equal sides and equal angles called ……….
Answer: regular polygon
38. Number of lines of symmetry of regular hexagon has……….
Answer: 6
39. A regular hexagon has all its sides equal and each of its angle measure is…….
Answer: 60°
40. Rotation turns an object about a fixed point. This fixed point is called……
Answer: centre of rotation
41. The angle by which the object rotates is called the……
Answer: angle of rotation
42. The order of rotational symmetry of is…..
Answer: 4
43. The angle of symmetry of adjacent figure is……
The angle of symmetry of adjacent figure is
Answer:120°
44. Each of the letters H, N, S, and Z has a rotational symmetry of order……..
Answer: 2
45. The concept line of symmetry is closely related to ……reflection.
Answer: Mirror
46. The angle of rotational symmetry for letter ‘S’ is……
Answer: 180°
47. Each regular polygon has as many lines of symmetry as it has…….
Answer: number of sides
48. The order of rotational symmetry……….
Answer:  \( \left[\frac{360^{\circ}}{x^0}\right] \)
49. The angle of rotational symmetry of adjacent figure is………..
The angle of rotational symmetry of adjacentfigure is
Answer: 90°
50. Match the following:
     
 Shape                                                                                             No. of lines of symmetry
1. Rhombus                                                                                               (  ) A) 2
2. Rectangle                                                                                              (  ) B) 0
3. Order of rotational symmetry of an equilateral triangle is              (  ) C) 4
4. A parallelogram                                                                                    (  ) D) 1
5. An isosceles triangle                                                                             (  ) E) 3
Answer:
1. C 2. A 3. E 4. B 5. D

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