1. SYMMETRY
SYMMETRY
1.. Symmetry is an important concept which is seen in lots of places in mathematics.
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2.. There are several types of symmetry:
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 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
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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.
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You can place a mirror along a line of symmetry and get an exact copy of the
original shape.
5.. Lines of symmetry
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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. QUADRIILATERALS
QUADR LATERALS
SQUARE has four lines of symmetry
SQUARE
RECTANGLE has two lines of symmetry
RECTANGLE
PARALLELOGRAM has no line of symmetry
PARALLELOGRAM
IISOSCELES TRAPEZOIID has one line of symmetry
SOSCELES TRAPEZO D
REGULAR HEXAGON has 6 lines of symmetry
REGULAR HEXAGON
str. 2

3. The dashed lines below are lines of symmetry.
CIIRCLE has infinite lines of symmetry
C RCLE
6.. Point symmetry is when every part has a matching part:
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 the same distance from the central point
 but in the opposite direction
7.. Rotational symmetry
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To 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 the
figure in a counterclockwise direction so that it looks the same as it does in its original
position.
8.. When a figure is rotated between 0° and 360°, the resulting figure coincides with
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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. 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