Question 1 - Think & Reflect (Page 94) - Symmetries of Circle - Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja

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Question 1 - Think & Reflect (Page 94) What are the rotational symmetries of a square? How many lines of reflection symmetry does it have? What about a regular pentagon? A regular hexagon? Let’s look at it one by one Line of Symmetry - Square Thus, Square has 4 lines of symmetry Rotational Symmetry – Square In case of square, we rotate it about the center Let’s rotate it 90° Rotating a Square 90° Initial figure 90° 90° + 90° = 180° 270° + 90° = 360° 180° + 90° = 270° Thus, in 1 full turn (i.e 360°) The figure is same as that of initial 4 times So, we say that figure has Rotational Symmetry of order 4 And, Angle of symmetry = (𝟑𝟔𝟎° )/(𝑶𝒓𝒅𝒆𝒓 𝒐𝒇 𝑹𝒐𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒍 𝑺𝒚𝒎𝒎𝒆𝒕𝒓𝒚) = (360° )/4 = 90° Regular PentagonChecking line of symmetry Thus, this figure has 5 lines of symmetry And, it has also Rotational symmetry of order 5 i.e. Angles of symmetry = (360° )/5 = 72° Regular HexagonChecking line of symmetry Thus, this figure has 6 lines of symmetry And, it has also Rotational symmetry of order 6 i.e. Angles of symmetry = (360° )/6 = 60°