NCERT Solution for Class 7th Maths Exercise – 14.3 Chapter – 14 Symmetry

Q1. Name any two figures that have both line symmetry and rotational symmetry.

Solution:-

Equilateral triangle and circle.

Q2. Draw wherever possible , a rough sketch of

A triangle with both line and rotational symmetries of order more than 1.

Solution:-

A triangle with both line and rotational symmetries of order more than 1 is an equilateral triangle.

Line Symmetry

Rotational Symmetry

A triangle with only line symmetry and no rotational symmetry of order more than 1 .

Solution:-

A triangle with only line symmetry and no rotational symmetry of order more than 1. is isosceles triangle.

A quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry

Solution:-

A triangle with only time symmetry and no rational symmetry of order more than 1 is isosceles triangles .

III. A Quadrilateral with a rational symmetry of order more than 1 but not a line symmetry .

Solution:-

A quadrilateral with a rotational symmetry of order more than 1. but not a line symmetry is not possible to draw. Because , a quadrilateral with a line symmetry may have rotational symmetry of order one but not more than one.

A quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Solution:-

A quadrilateral with line symmetry but not a rotational symmetry of order more than 1 is rhombus.

Q3. If a figure has two or more lines of symmetry should it have rotational symmetry of order more than 1?

Solution:-

Yes. If a figure has two or more lines of symmetry then it will have rotational symmetry of order more than 1.

Q4. Fill in the blanks:

Shape	Centre of rotation	Order of rotation	Angle of rotation
Square
Rectangle
Rhombus
Equilateral triangle
Regular Hexagon
Circle
Semi – Circle

Solution:-

Shape	Centre of rotation	Order of rotation	Angle of rotation
Square	Intersecting point of diagonals	4	90^o
Rectangle	Intersecting point of diagonal	2	180^o
rhombus	Intersecting point of diagonals	2	180^o
Equilateral triangle	Intersecting point of medians	3	120^o
Regular hexagon	Intersecting point of diagonals	6	60^o
circle	centre	Infinite	Every angle
Semi-circle	Mid – point of diameter	1	360^o

q-5 Name the quadrilaterals which have both line and rotational symmetry of order more than 1 .

Solution:-

The quadrilateral which have both line and rational symmetry of order more than 1 is square .

Line symmetry:

Rotational symmetry :

Q-6 After rotating by 60^o 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^o, 180^o , 240^o, 300^o, 360^o

So, the figure is said to have rational symmetry about same angles as the first one . hence , the figure will look exactly the same when rotated by 60^o from the last position .

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