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SYMMETRY

SYMMETRY. What is symmetry?. Symmetry, in geometry is a correspondence or matching of parts of an object. These parts correspond in size, shape and position after certain geometric operations are carried out.

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SYMMETRY

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  1. SYMMETRY (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  2. What is symmetry? Symmetry, in geometry is a correspondence or matching of parts of an object. These parts correspond in size, shape and position after certain geometric operations are carried out. In other words, symmetry is when an object can be folded in half along a line of symmetry, and both sides match up perfectly. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  3. Important terms related to symmetry • Point of symmetry • It is the centre or midpoint of a symmetrical object. Located at equal distances from this point are equal and opposite pairs of parts. • Axis of symmetry • It is an imaginary line through the centre of an object. Rotating an object about this line produces a number of identical appearances when rotated 360° about its axis of symmetry. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  4. Plane of symmetry • Divides a 3D shape into two symmetrical parts. These parts are mirror images of each other. This means the reflection of one of the parts matches that of the other parts. This kind of symmetry is therefore called reflectional symmetry. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  5. Types of symmetry. There are various types of symmetry such as: • Reflectional symmetry (Bilateral) • Rotational symmetry (Radial) • Translational symmetry • Point symmetry (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  6. Reflectional symmetry • Reflectional symmetry is symmetry across a line of reflection. An image is said to have reflectional symmetry if there is at least one line that splits the image into half, so that one side is the mirror image of the other. • It is often referred to as bilateral symmetry, line symmetry or even mirror symmetry. • A reflection is sometimes called a FLIP. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  7. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  8. Rotational symmetry • An image has rotational symmetry if it fits onto itself more than once when rotated 360° from a fixed point in the centre. • The order of rotational symmetry is the number of times a figure fits onto itself when rotated through 360° • Every shape has rotational symmetry of order one as rotation through 360° will bring it back to its original position. • A rotation is sometimes called a TURN. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  9. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  10. Translational symmetry • An image is said to have translational symmetry if it ahs been moved a certain distance in a certain direction, also called translating by a vector. • A translation is sometimes called a SLIDE. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  11. Point symmetry • Point symmetry is when every part of a figure has a matching part that is: • The same distance from the origin • In the opposite direction • When a figure has point symmetry, it appears not to have moved after rotation through 180° • Point Symmetry is sometimes called Origin Symmetry, because the "Origin" is the central point about which the shape is symmetrical. (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  12. Examples of 2D symmetry (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  13. Examples of 3D symmetry (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  14. Symmetry in nature (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  15. Symmetry in daily life (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  16. Applications of symmetry • Designing tattoos • Designing rugs • Classifying crystals • Khangas • Table cloth designs (doilies) • Building hotels • Clothes • Spectacle frames • Ink spots for psychological tests • Making kites (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  17. Some sample questions Find the order of rotational symmetry of this symbol. ANSWER: ORDER OF ROTATION 3 Draw the line of symmetry for this figure. ANSWER:  (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

  18. Done by: • Disha C. Okhai • Anjli Bajaria • Mohammed Bhanji • Nish Bajaria 10B (C) Disha C. Okhai, Anjli Bajaria, Mohammed Bhanji and Nish Bajaria

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