Symmetry - Solutions 3

CBSE Class –VII Mathematics
NCERT Solutions
Chapter 14 Symmetry (Ex. 14.3)

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Question 1. Name any two figures that have both line symmetry and rotational symmetry.

Answer: Circle and Square.

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:

Rotational symmetry:

(ii) An isosceles triangle has only one line of symmetry and no rotational symmetry of order more than 1.

Line symmetry:

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:

Rotational symmetry:

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.

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: 

Shape	Centre of Rotation	Order of Rotation	Angle of Rotation
Square	Intersecting point of diagonals.	4	90∘${90}^{\circ }$
Rectangle	Intersecting point of diagonals.	2	180∘${180}^{\circ }$
Rhombus	Intersecting point of diagonals.	2	180∘${180}^{\circ }$
Equilateral triangle	Intersecting point of medians.	3	120∘${120}^{\circ }$
Regular hexagon	Intersecting point of diagonals.	6	60∘${60}^{\circ }$
Circle	Centre	infinite	At every point
Semi-circle	Mid-point of diameter	1	360∘${360}^{\circ }$

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:

Rotational symmetry:

Question 6. After rotating by 60∘${60}^{\circ }$ 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∘,180∘,240∘,300∘,360∘${120}^{\circ },{180}^{\circ },{240}^{\circ },{300}^{\circ },{360}^{\circ }$.

For rotation:It will rotate six times.

For rotation:It will rotate three times.

For rotation:It will rotate two times.

For rotation:It will rotate one time.

Question 7. Can we have a rotational symmetry of order more than 1 whose angle of rotation is:

(i) 45∘${45}^{\circ }$(ii) 17∘${17}^{\circ }$ ?

Answer: (i) If the angle of rotation is 45∘,${45}^{\circ },$ then symmetry of order is possible and would be 8 rotations.

(ii) If the angle of rotational is 17∘,${17}^{\circ },$ then symmetry of order is not possible because 360∘${360}^{\circ }$ is not complete divided by 17∘.