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# Symmetry 1

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### Symmetry 1

1. 1. SYMMETRY SYMMETRY1.. Symmetry is an important concept which is seen in lots of places in mathematics.12.. There are several types of symmetry:2  the butterfly is an example of reflectional symmetry  the fan blade is an example of rotational symmetry  the wall paper border is an example of translational symmetry 3.. Reflectional symmetry which is sometimes called mirror symmetry or line symmetry 3 is when one half is a mirror image of the other half. A figure has line symmetry if a line can be drawn through the figure so that each half is a mirror image of the other. 4.. The figure has a line of symmetry that divides the figure into two congruent halves. 4 You can place a mirror along a line of symmetry and get an exact copy of the original shape. 5.. Lines of symmetry 5 TRIIANGLES TR ANGLES A SCALENE SCALENE An IISOSCELES SOSCELES An EQUIILATERAL EQU LATERAL TRIIANGLE (no sides TR ANGLE TRIIANGLE (two sides TR ANGLE TRIIANGLE (all sides TR ANGLE equal, no angles equal, two angles equal, all angles equal) has no lines of equal) has one line of equal) has three lines symmetry symmetry of symmetry str. 1
2. 2. QUADRIILATERALS QUADR LATERALSSQUARE has four lines of symmetrySQUARERECTANGLE has two lines of symmetryRECTANGLEPARALLELOGRAM has no line of symmetryPARALLELOGRAMIISOSCELES TRAPEZOIID has one line of symmetry SOSCELES TRAPEZO DREGULAR HEXAGON has 6 lines of symmetryREGULAR HEXAGON str. 2
3. 3. The dashed lines below are lines of symmetry.CIIRCLE has infinite lines of symmetryC RCLE 6.. Point symmetry is when every part has a matching part: 6  the same distance from the central point  but in the opposite direction 7.. Rotational symmetry 7To describe the rotation symmetry in a figure, you need to specify two things:• The center of rotation - this is the fixed point about which you rotate the figure.• The angle of rotation - this is the smallest angle through which you can turn thefigure in a counterclockwise direction so that it looks the same as it does in its originalposition.8.. When a figure is rotated between 0° and 360°, the resulting figure coincides with8 the original. a) The smallest angle through which the figure is rotated to coincide with itself is called the angle of rotational symmetry. b) The number of times that you can get an identical figure when repeating the degree of rotation is called the order of the rotational symmetry. angle: 180° 120° no rotational order: 2 3 symmetry str. 3
4. 4. Rotational symmetry can be found in many objects that rotate about a centerpoint.For example the automobile hubcaps shown have rotational symmetry.A dartboard has rotational symmetry of order 10 str. 4