Question

Let us draw plane figures, then cut them off to find if they have rotational symmetry? Let's write in the blank space given below and try to verify them.

Plane figure	Let's draw a small figure	Centre of rotation	Angle of rotation symmetry	Degree of rotation symmetry
Equilateral triangle	_____	_____	_____	_____
Square		Point of intersection of diagonals or intersection of the lines joining the midpoints of opposite sides	_____	_____
Rectangle		_____	_____	_____
Trapezium	_____	_____	_____	_____
Parallelogram	_____	Point of intersection of the diagonals	$180 °$	$2$
Rhombus	_____	Point of intersection of the diagonals	$180 °$	$2$
Regular pentagon		Intersection of lines joining the vertex with mid-point of opposite side.	$\frac{360 °}{5} = 72 °$	_____
Regular hexagon		_____	_____	_____

Accepted Answer

We know that, the centre of rotation is a point about which a plane figure rotates.

The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself.

And the number of times that it can be rotated is called the order of symmetry.

So, the complete table is given as below:

Plane figure Let's draw a small figure Centre of rotation Angle of rotation symmetry Order of rotation symmetry

Equilateral triangle
Point of intersection of its angle bisectors/altitudes/median.
$\frac{360 °}{3} = 120 °$ $3$

Square Point of intersection of diagonals $\frac{360 °}{4} = 90 °$ $4$

Rectangle Point of intersection of diagonals $\frac{360 °}{2} = 180 °$ $2$

Trapezium Point of intersection of diagonals $\frac{360 °}{1} = 360 °$ $1$

Parallelogram Point of intersection of the diagonals $180 °$ $2$

Rhombus Point of intersection of the diagonals $180 °$ $2$

Regular pentagon Intersection of lines joining the vertex with mid-point of opposite side. $\frac{360 °}{5} = 72 °$ $5$

Regular hexagon Point of intersection of diagonals $\frac{360 °}{6} = 60 °$ $6$

West Bengal Board Solutions for Chapter: Symmetry, Exercise 6: Exercise 6

West Bengal Board Mathematics Solutions for Exercise - West Bengal Board Solutions for Chapter: Symmetry, Exercise 6: Exercise 6

Questions from West Bengal Board Solutions for Chapter: Symmetry, Exercise 6: Exercise 6 with Hints & Solutions

Learn and Prepare for any exam you want !