Exercise 12.3 (Revised) - Chapter 14 - Symmetry - Ncert Solutions class 7 - Maths
Updated On 26-08-2025 By Lithanya
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Chapter 12: Symmetry - NCERT Solutions for Class 7 Maths
Ex 12.3 Question 1.
Name any two figures that have both line symmetry and rotational symmetry.
Answer:
Circle and Square.
Ex 12.3 Question 2.
Draw, wherever possible, a rough sketch of:
1. a triangle with both line and rotational symmetries of order more than one.
2. a triangle with only line symmetry and no rotational symmetry of order more than one.
3 .a quadrilateral with a rotational symmetry of order more than one but not a line symmetry.
4. a quadrilateral with line symmetry but not a rotational symmetry of order more than one.
Answer:
(i) An equilateral triangle has both line and rotational symmetries of order more than one.
Line symmetry:
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Rotational symmetry:
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(ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1 .
.png)
Line symmetry:
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Rotational symmetry:
(iii) It is not possible because order of rotational symmetry is more than 1 of a figure, most acertain the line of symmetry.
(iv) A trapezium which has equal non-parallel sides, a quadrilateral with line symmetry but not a rotational symmetry of order more than 1 .
Line symmetry:
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Rotational symmetry:
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Ex 12.3 Question 3.
In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1 ?
Answer:
Yes, because every line through the centre forms a line of symmetry and it has rotational symmetry around the centre for every angle.
Ex 12.3 Question 4.
Fill in the blanks:
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Answer:
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Ex 12.3 Question 5.
Name the quadrilateral which has both line and rotational symmetry of order more than 1 .
Answer:
Square has both line and rotational symmetry of order more than 1 . Line symmetry:
.png)
Rotational symmetry:
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Ex 12.3 Question 6.
After rotating by $60^{\circ}$ about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?
Answer:
Other angles will be $120^{\circ}, 180^{\circ}, 240^{\circ}, 300^{\circ}, 360^{\circ}$.
For rotation:It will rotate six times.
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For rotation:It will rotate three times.
.png)
For rotation:It will rotate two times.
.png)
For rotation:It will rotate one time.
.png)
Ex 12.3 Question 7.
Can we have a rotational symmetry of order more than 1 whose angle of rotation is:
(i) $45^{\circ}$ (ii) $17^{\circ}$ ?
Answer:
(i) If the angle of rotation is $45^{\circ}$, then symmetry of order is possible and would be 8 rotations.
(ii) If the angle of rotational is $17^{\circ}$, then symmetry of order is not possible because $360^{\circ}$ is not complete divided by $17^{\circ}$.
