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

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

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.

In other words, symmetry is when an object can be folded in half along a line of symmetry, and both sides match up perfectly.


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.


• 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.


Types of symmetry.

There are various types of symmetry such as:

• Reflectional symmetry (Bilateral)

• Rotational symmetry (Radial)

• Translational symmetry

• Point symmetry


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.



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.



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.


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.


Examples of 2D symmetry


Examples of 3D symmetry


Symmetry in nature


Symmetry in daily life


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


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:


Done by:

• Disha C. Okhai

• Anjli Bajaria

• Mohammed Bhanji

• Nish Bajaria

10B

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