NCERT Solutions for Class 7 Maths Chapter 14 Symmetry
NCERT Solutions for Class 7 Maths Chapter 14 Symmetry- In mathematics, s ymmetry means that one shape becomes exactly like another when you move(turn, flip or slide) it in some way. In nature, tree-leaves, beehives, flowers, and in the logo, symbols everywhere you can find various types of symmetrical designs. In this article, you will get CBSE NCERT solutions for class 7 maths chapter 14 symmetry. It is an important concept of the geometrical part used in artists, designing of jewelry or clothes, architects, car manufacturers, etc. In this chapter, you will learn some basic symmetry concepts like line symmetry, lines of symmetry for regular polygons, and rotational symmetry.
- Line of Symmetry:- It is defined as the imaginary line or axis that passes through the center of the object or shape and divides it into two perfectly identical halves. Example-Regular polygons like square, regular pentagon, a regular hexagon, etc have equal sides and equal angles. They have more than one line of symmetry.
Number of lines of symmetry of some regular polygon are given in the following table-
Regular polygon | Regular hexagon | Regular pentagon | Square | Equilateral triangle |
No. of lines of symmetry | 6 | 5 | 4 | 3 |
- Rotational symmetry:- It is defined as the imaginary a center point (fixed point) around that an object or shape is rotated by a number of degrees and the object or shape looks exactly the same. In a complete turn of 360-degree, the number of times an object or shape looks exactly the same is called the order of rotational symmetry.
The order of symmetry for an equilateral triangle is 3 and the order of symmetry for a square is 4. In NCERT solutions for class 7 maths chapter 14 symmetry, you will get many questions related to the order of symmetry which will give you more clarity of the concept. In this chapter of NCERT, there are 19 questions in three exercises. You will get detailed explanations of all these questions in CBSE NCERT solutions for class 7 maths chapter 14 symmetry. It will be very easy for you to understand the concept. You can get NCERT solutions from class 6 to 12 by clicking on the above link. Here you will get NCERT solutions for class 7 .
Topics of NCERT Grade 7 Maths Chapter 14 Symmetry
14.1 Introduction
14.2 Lines of Symmetry for Regular Polygons
14.3 Rotational Symmetry
14.4 Line Symmetry and Rotational Symmetry
NCERT solutions for class 7 maths chapter 14 symmetry exercise 14.1
Question:1 .(a) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question:1.(b) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1.(c) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1.(d) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1 .(e) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1 (f) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1 (g) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1( h) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry are as shown :
Question: 1(i) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1(j) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 1.(k) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question:1.(l) Copy the figures with punched holes and find the axes of symmetry for the following:
Answer:
The axes of symmetry is as shown :
Question: 2 Given the line(s) of symmetry, find the other hole(s):
Answer:
The other holes from the symmetry are as shown :
Answer:
The complete figures are as shown :
(a) square (b)triangle (c)rhombus
(d)circle (e) pentagon (f) octagon
Identify multiple lines of symmetry, if any, in each of the following figures:
Answer:
The lines of symmetry of figures are:
(a)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.
(b) There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.
(c)There are 3 lines of symmetry. Thus, it has multiple lines of symmetry.
(d)There are 2 lines of symmetry. Thus, it has multiple lines of symmetry.
(e)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.
(f)There is 1 line of symmetry.
(g)There are 4 lines of symmetry. Thus, it has multiple lines of symmetry.
(h)There are 6 lines of symmetry. Thus, it has multiple lines of symmetry.
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:
The figure with symmetry may be as shown :
Yes,there more than one way .
Yes,the figure be symmetric about both the diagonals
Question: 6 Copy the diagram and complete each shape to be symmetric about the mirror line(s):
Answer:
The complete shape symmetric about the mirror line(s) are :
Question: 7 State the number of lines of symmetry for the following figures:
Answer:
(a) An equilateral triangle
The number of lines of symmetry = 3
(b) An isosceles triangle
The number of lines of symmetry = 1
(c) A scalene triangle
The number of lines of symmetry = 0
(d) A square
The number of lines of symmetry = 4
(e) A rectangle
The number of lines of symmetry = 2
(f) A rhombus
The number of lines of symmetry = 2
(g) A parallelogram
The number of lines of symmetry = 0
(h) A quadrilateral
The number of lines of symmetry = 0
(i) A regular hexagon
The number of lines of symmetry = 6
(j) A circle
The number of lines of symmetry = infinite
(c) both horizontal and vertical mirrors
Answer:
(a) 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 mirrors : H,I,O and X.
Question: 9 Give three examples of shapes with no line of symmetry.
Answer:
The three examples of shapes with no line of symmetry are :
1. Quadrilateral
2. Scalene triangle
3.Parallelogram
Question:1 0.(a) What other name can you give to the line of symmetry of
Answer:
The line of symmetry of an isosceles triangle is median or altitude.
Question: 10.(b) What other name can you give to the line of symmetry of
Answer:
The other name we can give to the line of symmetry of a circle is the diameter.
NCERT solutions for class 7 maths chapter 14 symmetry topic 14.3
Question: 1.(a) Can you now tell the order of the rotational symmetry for an equilateral triangle?
Answer:
An equilateral triangle has rotational symmetry at angle. The order of the rotational symmetry for an equilateral triangle is 3.
Question: 1.(b) How many positions are there at which the triangle looks exactly the same, when rotated about its centre by 120°?
Answer:
All the triangles look same when rotated by . Thus, there are 4 positions at which the triangle looks exactly the same when rotated about its centre by 120°.
Question:2 Which of the following shapes (Fig 14.15) have rotational symmetry about the marked point.
Answer:
Among the above-given shapes, (i),(ii) and (iv) have rotational symmetry about the marked point.
NCERT solutions for class 7 maths chapter 14 symmetry exercise 14.2
Question: 1 Which of the following figures have rotational symmetry of order more than 1:
Answer:
Among the above-given shapes, (a),(b), (d),(e) and (f) have more than one rotational symmetry.
This is because, in these figures, a complete turn, more than 1 number of times, an object look exactly the same.
Question: 2 Give the order of rotational symmetry for each figure:
Answer:
(a) The given figure has rotational symmetry about so it has ordered as 2.
(b) The given figure has rotational symmetry about so it has ordered as 2.
(c) The given figure has rotational symmetry about so it has ordered as 3.
(d) The given figure has rotational symmetry about so it has ordered as 4.
(e) The given figure has rotational symmetry about so it has ordered as 4.
(f) The given figure has rotational symmetry about so it has ordered as 5.
(g) The given figure has rotational symmetry about so it has ordered as 6.
(h) The given figure has rotational symmetry about so it has ordered as 3.
NCERT solutions for class 7 maths chapter 14 symmetry exercise 14.3
Question: 1 Name any two figures that have both line symmetry and rotational symmetry.
Answer:
The two figures that have both line symmetry and rotational symmetry are :
(i) Equilateral triangle
(ii) Regular hexagon
Question:2(i) Draw, wherever possible, a rough sketch of
a triangle with both line and rotational symmetries of order more than 1.
Answer:
Line of symmetry as shown below :
The rotational symmetry as shown below :
Question: 2(ii) Draw, wherever possible, a rough sketch of
a triangle with only line symmetry and no rotational symmetry of order more than 1.
Answer:
A triangle with only line symmetry and no rotational symmetry of order more than 1 is isosceles triangle.
Question:2(iii) Draw, wherever possible, a rough sketch of
a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
Answer:
A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry is parallelogram.
Question: 2(iv) Draw, wherever possible, a rough sketch of
a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Answer:
A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is kite.
Answer:
Yes. If a figure has two or more lines of symmetry,than it should have rotational symmetry of order more than 1.
Question: 4 Fill in the blanks:
Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
Square | |||
Rectangle | |||
Rhombus | |||
Equilateral Triangle | |||
Regular Hexagon | |||
Circle | |||
Semi-circle |
Answer:
The given table is completed as shown:
Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
Square | intersection point of digonals. | 4 | |
Rectangle | Intersection point of digonals. | 2 | |
Rhombus | Intersection point of digonals. | 2 | |
Equilateral Triangle | Intersection point of medians. | 3 | |
Regular Hexagon | Intersection point of digonals. | 6 | |
Circle | centre of circle | infinite | any angle |
Semi-circle | centre of circle | 1 |
Question: 5 Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer:
The quadrilaterals which have both line and rotational symmetry of order more than 1 are :
1. Rectangle
2. Square
3. Rhombus
Answer:
After rotating by about a centre, a figure looks exactly the same as its original position, then it will look symmetrical on rotating by All angles are multiples of .
Question: 7 Can we have a rotational symmetry of order more than 1 whose angle of rotation is:
Answer:
We can observe that the angle of rotation is the factor of ,then it will have rotational symmetry of order more than 1.
(i) is a factor of so the figure having its angle of rotation as will have rotational symmetry of order more than 1.
(ii) is not a factor of so the figure having its angle of rotation as will not have rotational symmetry of order more than 1.
NCERT Solutions for Class 7 Maths Chapter wise
NCERT Solutions for Class 7 Subject wise
Benefits of NCERT solutions for class 7 maths chapter 14 symmetry
- You will learn to identify different types of symmetry and also the order of the symmetry.
- It will make your homework easy as you will find the detailed explanations of all the NCERT questions including practice questions given below every topic in this article.
- You should try to solve all the NCERT questions including examples. If you facing difficulties in solving them, you can take help from these solutions.
- After every topic, there are some practice questions given in the textbook to give you conceptual clarity. In NCERT solutions for class 7 maths chapter 14 symmetry, you will find solutions to these practice questions also.
Happy learning!!!
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