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RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry

RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Free Online

Exercise 18.1 Page No: 18.6
1. State the number of lines of symmetry for the following figures:
(i) An equilateral triangle
(ii) An isosceles triangle
(iii) A scalene triangle
(iv) A rectangle
(v) A rhombus
(vi) A square
(vii) A parallelogram
(viii) A quadrilateral
(ix) A regular pentagon
(x) A regular hexagon
(xi) A circle
(xii) A semi-circle
Solution:
(i) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an equilateral triangle has 3 lines of symmetry.
(ii) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an isosceles triangle has 1 line of symmetry.
(iii) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a scalene triangle has no line of symmetry.
(iv) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rectangle has 2 lines of symmetry.
(v) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rhombus has 2 lines of symmetry.
(vi) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a square has 4 lines of symmetry.
(vii) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a parallelogram has no line of symmetry.
(viii) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a quadrilateral has no line of symmetry.
(ix) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular pentagon has 5 lines of symmetry.
(x) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular hexagon has 6 lines of symmetry.
(xi) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a circle has an infinite number of lines of symmetry all along the diameters.
(xii) If a line divides a figure into two parts such that when the figure is folded about the line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a semicircle has only one line of symmetry.
2. What other name can you give to the line of symmetry of
(i) An isosceles triangle?
(ii) A circle?
Solution:
(i) An isosceles triangle has only 1 line of symmetry. This line of symmetry is also known as the altitude of an isosceles triangle.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 1
(ii) A circle has infinite lines of symmetry all along its diameters.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 2
3. Identify three examples of shapes with no line of symmetry.
Solution:
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 3
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 4
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 5
A scalene triangle, a parallelogram and a trapezium do not have any line of symmetry.
4. Identify multiple lines of symmetry, if any, in each of the following figures:
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 6
Solution:
(A)The given figure has 3 lines of symmetry. Therefore it has multiple lines of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 7
(B) The given figure has 2 lines of symmetry. Therefore it has multiple lines of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 8
(C) The given figure has 3 lines of symmetry. Therefore it has multiple lines of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 9
(D) The given figure has 2 lines of symmetry. Therefore it has multiple lines of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 10
(E) The given figure has 4 lines of symmetry. Therefore it has multiple lines of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 11
(F) The given figure has only 1 line of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 12
(G) The given figure has 4 lines of symmetry. Therefore it has multiple lines of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 13
(H) The given figure has 6 lines of symmetry. Therefore it has multiple lines of symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 14

Exercise 18.2 Page No: 18.8
1. In the following figures, the mirror line (i.e. the line of symmetry) is given as dotted line. Complete each figure performing reflection in the dotted (mirror) line. Also, try to recall name of the complete figure.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 15
Solution:
(a) It will be a rectangle.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 16
(b) It will be triangle
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 17
(c) It will be rhombus
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 18
(d) It will be circle
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 19
(e) It will be pentagon
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 20
(d) It will be octagon
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 21
2. Each of the following figures shows paper cuttings with punched holes. Copy these figures on a plane sheet and mark the axis of symmetry so that if the paper is folded along it, then the wholes on one side of it coincide with the holes on the other side.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 22
Solution:
The lines of symmetry in the given figures are as follows:
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 23
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 24
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 25
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 26
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 27
3. In the following figures if the dotted lines represent the lines of symmetry, find the other hole(s).
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 28
Solution:
The other holes in the figure are as follows:
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 29

Exercise 18.3 Page No: 18.16
1. Give the order of rotational symmetry for each of the following figures when rotated about the marked point (x):
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 30
Solution:
(i) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 4.
(ii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 3.
(iii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 3.
(iv) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 4.
(v) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 2.
(vi) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 4.
(vii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 5.
(viii) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 6.
(ix) A figure is said to have rotational symmetry if its fits onto itself more than once during a full turn that is rotation through 360o
Therefore the given figure has its rotational symmetry as 3.
2. Name any two figures that have both line symmetry and rotational symmetry.
Solution:
An equilateral triangle and a square have both lines of symmetry and rotational symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 31
3. Give an example of a figure that has a line of symmetry but does not have rotational symmetry.
Solution:
A semicircle and an isosceles triangle have a line of symmetry but do not have rotational symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 32
4. 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.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 33
5. 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.
6. What is the line of symmetry of a semi-circle? Does it have rotational symmetry?
Solution:
A semicircle (half of a circle) has only one line of symmetry. In the figure, there is one line of symmetry. The figure is symmetric along the perpendicular bisector I of the diameter XY. A semi-circle does not have any rotational symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 34
7. Draw, whenever possible, a rough sketch of
(i) a triangle with both line and rotational symmetries.
(ii) a triangle with only line symmetry and no rotational symmetry.
(iii) a quadrilateral with a rotational symmetry but not a line of symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry.
Solution:
(i) An equilateral triangle has 3 lines of symmetry and a rotational symmetry of order 3.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 35
(ii) An isosceles triangle has only 1 line of symmetry and no rotational symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 36
(iii) A parallelogram is a quadrilateral which has no line of symmetry but a rotational symmetry of order 2.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 37
(iv) A kite is a quadrilateral which has only one line of symmetry and no rotational symmetry.
RD Sharma Solutions for Class 7 Maths Chapter 18 Symmetry Image 38
8. Fill in the blanks:
Figures
Centre of rotation
Order of rotation
Angle of rotation
Square
Rectangle
Rhombus
Equilateral Triangle
Regular hexagon
Circle
Semi-circle
Solution:
Figures
Centre of rotation
Order of rotation
Angle of rotation
Square
Point of intersection of the line segments joining the mid-points of opposite sides.
4
90o
Rectangle
Point of intersection of the line segments joining the mid-points of opposite sides
2
180o
Rhombus
Point of intersection of diagonals
2
180o
Equilateral Triangle
Point of intersection of angle bisectors i.e., centroid
3
1200
Regular hexagon
Centre of the hexagon
6
60o
Circle
Centre of the circle
Unlimited
Any angle
Semi-circle
Nil
Nil
Nil
9. Fill in the blanks:
English Alphabet Letter
Line Symmetry
Number of Lines of Symmetry
Rotational symmetry
Order of rotational symmetry
Z
Nil
0
Yes
2
S
H
Yes
Yes
O
Yes
Yes
E
Yes
N
Yes
C
Solution:
English Alphabet Letter
Line Symmetry
Number of Lines of Symmetry
Rotational symmetry
Order of rotational symmetry
Z
Nil
0
Yes
2
S
Nil
0
Yes
2
H
Yes
2
Yes
2
O
Yes
4
Yes
2
E
Yes
1
No
0
N
Nil
0
Yes
2
C
Yes
1
No
0
Courtesy : CBSE