Rotational Symmetry

Transcript

Rotational SymmetryLet’s look at a Paper Windmill This figure looks symmetrical, but has no line symmetry But, If we rotate it 90° from the center, the figure looks the same So, we can say it has Rotational Symmetry Let’s try to check actual Rotation Checking Rotation of Paper Windmill We Mark its edges as A, B, C, D Mark a reference line Then rotate it 90° clockwise from center – along a refrence line After 1st Rotation The figure looks same as previous – but points are moved around Let’s rotate 90° again (from reference line) After 2nd Rotation The figure looks same as previous – but points are moved around Let’s rotate 90° again (from reference line) After 2nd Rotation The figure looks same as previous – but points are moved around Let’s rotate 90° again (from reference line) After 3rd Rotation The figure looks same as previous – but points are moved around Let’s rotate 90° again (from reference line) After 4th Rotation The figure looks same as previous Here, it becomes the original figure Thus, after 4 rotations we get to the exact same position To Summarise 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° Thus, the figure would be same at angles 90° 90° × 2 = 180° 90° × 3 = 270° 90° × 4 = 360° So, we write Angles of symmetry = 90°, 180°, 270°, 360°