NCERT Solutions for Class 7 Maths Chapter 12 Symmetry Ex 12.3 (Rationalised Contents)
NCERT Solutions for Class 7 Maths Chapter 12 Symmetry Ex 12.3 are the part of NCERT Solutions for Class 7 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 7 Maths Chapter 12 Symmetry Ex 12.3.
- NCERT Solutions for Class 7 Maths Chapter 12 Symmetry Ex 12.1
- NCERT Solutions for Class 7 Maths Chapter 12 Symmetry Ex 12.2
- NCERT Solutions for Class 7 Maths Chapter 12 Symmetry Ex 12.3
Ex 12.3 Class 7 Maths Question 1.
Name any two figures that have both line symmetry and rotational symmetry.
Solution:
An equilateral triangle and a square both have line symmetry and rotational symmetry.
Ex 12.3 Class 7 Maths Question 2.
Draw, wherever possible, a rough sketch of
(i) a triangle with both line and rotational symmetries 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.
(iv) An isosceles trapezium has one line of symmetry and no rotational symmetry.
Ex 12.3 Class 7 Maths Question 3.
If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Solution:
Ex 12.3 Class 7 Maths Question 4.
Fill in the blanks:
Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
Square |
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Rectangle |
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Rhombus |
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Equilateral triangle |
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Regular hexagon |
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Circle |
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Semi-circle |
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Solution:
Shape | Centre of Rotation | Order of Rotation | Angle of Rotation |
Square | Point of intersection of diagonals | 4 | 90° |
Rectangle | Point of intersection of diagonals | 2 | 180° |
Rhombus | Point of intersection of diagonals | 2 | 180° |
Equilateral triangle | Point of intersection of medians | 3 | 120° |
Regular hexagon | Point of intersection of diagonals | 6 | 60° |
Circle | Centre | Infinite | Every angle |
Semi-circle | Centre | 1 | 360° |
Ex 12.3 Class 7 Maths Question 5.
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Solution:
A square, a rectangle and a rhombus are such quadrilaterals which have both line and rotational symmetry of order more than 1.
Ex 12.3 Class 7 Maths 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:
Since the figure looks exactly the same as its original position, when rotated through 60° about its centre, the angle of rotation is 60°. If the figure is rotated through the angles 120°, 180°, 240°, 300° and 360°, it looks exactly the same.
Ex 12.3 Class 7 Maths 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; because 360° is divisible by 45°.
(ii) No; because 360° is not divisible by 17°.
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