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NCERT Solutions for Maths Chapter 14 Symmetry Class 7: In mathematics, symmetry 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 class 7th maths chapter 14 solution . It is an important concept of the geometrical part used in artists, designing of jewellery or clothes, architects, car manufacturers, etc. 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. You can get NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get NCERT Solutions for Class 7. It is advisable that you must complete the NCERT Class 7 Maths Syllabus as soon as possible and then refer to the given solutions.
Angle of Rotation in regular polygon = 360°/Number of sides
A half-turn = Rotation by 180°
A quarter-turn = Rotation by 90°
Reflection in the x-axis , ( X , Y ) → ( X , -Y )
Reflection in the y-axis , ( X , Y ) → ( -X , Y )
Line Symmetry:
If it can be divided into two identical parts by a line, there will be a line of symmetry.
Regular polygons have equal angles and equal sides so they have multiple lines of symmetry. The table given below shows the number of lines of symmetry in regular polygons.
Regular Polygons | Regular Hexagon | Regular Pentagon | Square | Equilateral Triangle |
Number of the line of Symmetry | 6 | 5 | 4 | 3 |
Angle of Rotation in regular polygon = 360°/Number of sides
Rotational Symmetry: When we rotate an object if it looks exactly the same , we say that it has rotational symmetry.
Centre of rotation: That fixed point about which object rotates.
Angles of rotation: The angle by which the object rotates.
Order of Rotational Symmetry:
The number of times an object looks exactly the same, in a complete turn
(360°) is called the order of rotational symmetry.
Some objects have only line of symmetry ( like letter E), some objects have only rotational symmetry ( like the letter S), and some have both symmetries ( like the letter H).
Formulas for Reflection:
Reflection in the x-axis , ( X , Y ) → ( X , -Y )
Reflection in the y-axis , ( X , Y ) → ( -X , Y )
Free download NCERT Solutions for Class 7 Maths Chapter 14 Symmetry PDF for CBSE Exam.
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
(c) circle (d) pentagon (e) 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 :
The figure with symmetry may be as shown :
Yes,there more than one way .
Yes,the figure be symmetric about both the diagonals
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:
(a) An equilateral triangle (b) An isosceles triangle (c) A scalene triangle
(d) A square (e) A rectangle (f) A rhombus
(g) A parallelogram (h) A quadrilateral (i) A regular hexagon
(j) A circle
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
(a) a vertical mirror
(b) a horizontal mirror
(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:10.(a) What another name can you give to the line of symmetry of an isosceles triangle?
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
a circle?
Answer: The other name we can give to the line of symmetry of a circle is the diameter.
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.
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.
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 a 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.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | Symmetry |
Chapter 15 |
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