NCERT Solutions for Class 7 Maths Chapter 14 Symmetry, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 14 Symmetry.
NCERT Solutions for Class 7 Maths Chapter 14 Symmetry
NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.1
Question 1.
Copy the figures with punched holes and find the axes of symmetry for the following :
Solution:
Question 2.
Given the line(s) of symmetry, find the other hole(s) :
Solution:
Question 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 ?
Solution:
Question 4.
The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry :
Identify multiple lines of symmetry, if any, in each of the following figures :
Solution:
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?
Solution:
Yes! there is more than one way to make the figure symmetric.
(i) Let us take the diagonal BD and shade the squares as shown in the figure to make the figure symmetric about BD.
(ii) Similarly, the figure is symmetric about the diagonal AC.
Thus, the figure is symmetric about both the diagonals.
(iii) The figure is symmetric about EF and GH also.
Question 6.
Copy the diagram and complete each shape to be symmetric about the mirror line(s) :
Solution:
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.
Solution:
Question 8.
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.
Solution:
Question 9.
Give three examples of shapes with no line of symmetry.
Solution:
(b) A scalene triangle,
(c) A parallelogram
Question 10.
What other name can you give to the line of symmetry of
(a) an isosceles triangle?
(b) a circle?
Solution:
(a) Median
(b) Diameter.
NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.2
Question 1.
W
hich of the following figures have rotational symmetry of order more than 1?
Solution:
Figures (a), (b), (d), (e) and (f) have rotational symmetry of order more than 1.
Question 2.
Give the order of rotational symmetry for each figure :
Solution:
(a) → 2
(b) → 2
(c) → 3
(d) → 4
(e) → 4
(f) → 5
(g) → 6
(h) → 3
Mark a point P as shown in figure (i). We see that in a full turn, there are two positions (on rotation through the angles 180° and 360°) when the figure looks exactly the same.
Because of this, it has a rotational symmetry of order 2.
Mark a point P as shown in figure (i). We see that in a full turn, there are two positions (on rotation through the angles 180° and 360°) when the figure looks exactly the same.
Because of this, it has a rotational symmetry of order 2.
Mark a point P as shown in figure (i). We see that in a full turn, there are three positions (on rotation through the angles 120°, 240° and 360°) when the figure looks exactly the same.
Because of this, it has a rotational symmetry of order 3.
Mark a point P as shown in figure (i).
We see that in a full turn, there are four positions (on rotation through the angles 90°, 180°, 270° and 360°) when the figure looks exactly the same.
Because of this, we say that it has a rotational symmetry of order 4.
Similarly,
(e) In a full turn, there are four positions (on rotation through the angles 90°, 180°, 270° and 360°) when the figure looks exactly the same.
∴ It has a rotational symmetry of order 4.
(f) The figure is a regular pentagon. In a full turn, there are five positions (on rotation through the angles 72°, 144°, 216°, 288° and 360°) when the figure looks exactly the same.
∴ It has a rotational symmetry of order 5.
(g) In a full turn, there are six positions (on rotation through the angles 60°, 120°, 180°, 240°, 300° and 360°) when the figure looks exactly the same.
It has a rotational symmetry of order 6.
(h) In a full turn, there are three positions (on rotation through the angles 120°, 240° and i 360°) when the figure looks exactly the same.
∴ It has a rotational symmetry of order 3.
NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3
Question 1.
Name any two figures that have both line symmetry and rotational symmetry.
Solution:
- Circle
- Equilateral triangle
Question 2.
Draw, wherever possible, a rough sketch of
(i) a triangle with both line and rotational symmetry of order more than 1.
(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.
(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Solution:
(i) An equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.
(ii) An isosceles triangle has only one line symmetry but no rotational symmetry of order more than 1.
(iii) A parallelogram has no line of symmetry but has a rotational symmetry of order 2.
(iv) An isosceles trapezium has one line of symmetry but no rotational symmetry of order more than 1.
Question 3.
If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1 ?
Solution:
Yes.
Question 4.
Fill in the blanks :
Solution:
Question 5.
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Solution:
- Square
- Rectangle
Question 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°.
Question 7.
Can we have a rotational symmetry of order more than 1 whose angle of rotation is (i)45°? (ii)17°?
Solution:
(i) Yes
(ii) No
NCERT Solutions for Class 7 Maths Chapter 14 Symmetry MCQ
Important Multiple Choice Questions
1. How many lines of symmetry are there in an equilateral triangle?
(a) 1
(b) 2
(c) 3
(d) 4.
2. How many lines of symmetry are there in a square?
(a) 1
(b) 2
(c) 3
(d) 4.
3. How many lines of symmetry are there in a rectangle?
(a) 1
(b) 2
(c) 3
(d) 4.
4. How many lines of symmetry are there in a regular pentagon?
(a) 1
(b) 2
(c) 3
(d) 5.
5. How many lines of symmetry are there in a regular hexagon?
(a) 2
(b) 4
(c) 6
(d) 3.
6. How many lines of symmetry are there in the following figure?
(a) 1
(b) 2
(c) 3
(d) 4
7. How many lines of symmetry are there in the following figure?
(a) 1
(b) 2
(c) 3
(d) 4
8. How many lines of symmetry are there in the following figure?
(a) 1
(b) 2
(c) 3
(d) 4
9. How many lines of symmetry are there in the following figure?
(a) 4
(b) 3
(c) 2
(d) 1
10. How many lines of symmetry are there in the following figure?
(a) 2
(b) 1
(c) 4
(d) 3
11. How many lines of symmetry are there in following figure?
(a) 1
(b) 2
(c) 3
(d) None of these
12. How many lines of symmetry are there in the following figure?
(a) 1
(b) 2
(c) 3
(d) Infinitely many
13. How many lines of symmetry are there in an isosceles triangle?
(a) 4
(b) 3
(c) 1
(d) 2.
14. How many lines of symmetry are there in a scalene triangle?
(a) 1
(b) 0
(c) 2
(d) 4
15. How many lines of symmetry are there in a rhombus?
(a) 1
(b) 2
(c) 3
(d) 4
16. How many lines of symmetry are there in a parallelogram?
(a) 0
(b) 1
(c) 2
(d) None of these.
17. How many lines of symmetry are there in a quadrilateral?
(a) 0
(b) 2
(c) 4
(d) None of these.
18. The order of rotational symmetry of an equilateral triangle is
(a) 1
(b) 2
(c) 3
(d) 4
19. The order of rotational symmetry of a square is
(a) 1
(b) 2
(c) 3
(d) 4
20. What is the order of the rotational symmetry of the following figure?
(a) 4
(b) 3
(c) 2
(d) 1
21. The order of the rotational symmetry of the following figure about the point marked x (cross) is
(a) 1
(b) 2
(c) 3
(d) 4
22. The order of the rotational symmetry of the following figure about the point marked x is
(a) 1
(b) 2
(c) 3
(d) 4
23. The order of the rotational symmetry of the following figure about the point marked x is
(a) 2
(b) 3
(c) 4
(d) 1
24. Which of the following letters of English alphabet has reflectional symmetry about a vertical mirror?
(a) H
(b) J
(c) Z
(d) P.
25. Which of the following letters of English alphabet has reflectional symmetry about a horizontal mirror?
(a) H
(b) K
(c) M
(d) W
26. Which of the following letters of English alphabet has reflectional symmetry about both horizontal and vertical mirrors?
(a) O
(b) Y
(c) T
(d) L.
27. The quadrilateral which has both line and rotational symmetry of order more than 1 is
(a) isosceles triangle
(b) rhombus
(c) scalene triangle
(d) square.
ANSWERS
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