Ex 12.2, 1 (a) - Chapter 12 Class 7 Symmetry

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Ex 12.2, 1 (a) Which of the following figures have rotational symmetry of order more than 1: Let’s rotate it by 90° Again rotate it by 90° Suppose it rotate by 90° again Once more, it rotates by 90° Thus, in 1 full turn (i.e. 360°) The figure is same as that of initial 4 turns. So, we say that figure has rotational symmetry of order 4 Ex 12.2, 1 (b) Which of the following figures have rotational symmetry of order more than 1: Let’s rotate it by 120° This figure looks same as previous. Again, rotate it by 120° This figure looks same as previous Suppose, it rotates by 120° again This figure looks same as previous Thus, in 1 full turn (i.e. 360°) This figure is same as that of initial 3 turns So, we say that figure has rotational symmetry of order 3 Ex 12.2, 1 (c) Which of the following figures have rotational symmetry of order more than 1: Let’s rotate it by 180° This does not looks like previous figure Again rotating by 180° This looks like initial figure. So, this figure on rotational is same as initial figure only when it has rotated 360° So, it has the order of rotational symmetry 1 Ex 12.2, 1 (d) Which of the following figures have rotational symmetry of order more than 1: Let’s rotate it by 180° This figure looks same as previous Again, rotate it by 180° This figure looks same as previous Thus, Thus, in 1 full turn (i.e 360° ) This figure is same as that of initial 2 turns So, we say that figure has rotational symmetry of order 2 Ex 12.2, 1 (e) Which of the following figures have rotational symmetry of order more than 1: Since circle is divided into 3 equal sectors, Angle at center = (360°)/3 = 120° This figure looks same as previous Suppose it rotates 120° again This figure looks same as previous Again it rotates 120° This figure looks same as previous Ex 12.2, 1 (f) Which of the following figures have rotational symmetry of order more than 1: Let’s rotate it by 90° This figure looks same as previous. Again rotating it by 90° This figure looks same as previous. Again it rotates it by 90° This figure looks same as previous. Suppose it again rotates 90° This figure looks same as previous. Thus, in 1 full-turn (i.e. 360°) The figure is same as that of initial 4 turns So, we say that figure has rotational symmetry of order 4 Hence, figure (a), (b), (d), (e) and (f) have rotational symmetry of order more than one