Ex.14.3 Q2 Symmetry - NCERT Maths Class 7

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 rotational symmetry of order more than \(1\).

Text Solution

What is unknown?

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 rotational symmetry of order more than \(1\).

Reasoning:

To solve this question, remember the concept of rotational symmetry. Rotational symmetry is when an object is rotated around a centre point (turned) a number of degrees and the object appears the same. The order of symmetry is the number of positions the object looks the same in a \(360^\circ\) rotation.

Steps:

(i) An equilateral triangle has both line and rotational symmetry of order more than \(1.\)

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

(iii) Parallelogram has two order of rotational symmetry but no line of symmetry.

(iv) A kite is a quadrilateral which has only one line of symmetry but not rotational symmetry of order more than \(1.\)