Symmetry - as a common geometry expression means a figure looking same
under a transformation i.e.
is when a figure has two sides that
are mirror images of one another. It would then be possible to draw a
line through a picture of the object and along either side the image
would look exactly the same. This line would be called a line of
symmetry. E.g. the letter A is symmetrical under a reflection
around a vertical mirror through its center.
There are two kinds of symmetry. One is bilateral symmetry in which
an object has two sides that are mirror images of each other. Say an
equilateral triangle would be a geometric example of bilateral symmetry.
The other could be radial symmetry. In this case from the center
point numerous lines of symmetry can be drawn. E.g. a circle.
(More text below video...)
(Continued from above)
A figure has line symmetry when the figure is its own image under a line reflection.
This line of reflection is a line of symmetry, or an axis of symmetry.
Some properties of a line reflection by considering the reflection of
isosceles triangle ABC in line k are as follows:
1. Distance is preserved (unchanged). ABCB
and AB = CBADCD
and AD = CD
2. Angle measure is preserved. BADBCD
3. The line of reflection, is the perpendicular bisector of AC.
4. A figure is always congruent to its image:
Now you should be able to distinguish between congruent and similar,
as on transformation the two shapes might be congruent or similar.
Remember Theorems and Corollaries for the lesson
• Under a line reflection, distance is preserved.
• Under a reflection in the y-axis, the image of P (a, b) is P'
• Under a reflection in the x-axis, the image of P (a, b) is P'
• Under a reflection in the line y = x, the image of P (a, b)
is P' (b, a).
• Under a point reflection, distance is preserved.
• Under a reflection in the origin, the image of P (a, b) is P' (-a, -b).
• Under a translation, distance is preserved.
• Distance is preserved under a rotation about a fixed point.
• Under a counterclockwise rotation of
about the origin, the image of P (a, b) is P' (-b, a).
• Under a glide reflection, distance is preserved.
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