Geometry: Symmetry
This is a free lesson from our course in Geometry
 
   
Symmetry - as a common geometry expression means a figure looking same under a transformation i.e. symmetry 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...) Line_of_symmetry
<h2> Geometry - Symmetry </h2> <p> triangle, symmetery, polygon, sides, geometry, rotation, reflection, point, line, example, geometry, rectangle, regular equilateral, point symmetery, rotation symmetery, solution, isosceles, reflection symmetery, practice question, quizzes</p> <p> A figure has line symmetry, if it can be reflected about a line onto itself and each regular polygon has as many lines of symmetry as it has sides e.g. an equilateral triangle has three lines of symmetry.</p>
Other useful lessons:
Translation, Reflection, Dilation, and Rotation
(Continued from above) Line Symmetry: 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).
AB CB and  AB = CB   AD CD and AD = CD
2. Angle measure is preserved.
BAD BCD and mBAD mBCD 
 BDA BDC and mBDA mBDC
3. The line of reflection, is the perpendicular bisector of AC.
4. A figure is always congruent to its image: ABC CBA 		Line_symmetry_properties
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' (-a, b).
• Under a reflection in the x-axis, the image of P (a, b) is P' (a, -b).
• 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 90 about the origin, the image of P (a, b) is P' (-b, a).
• Under a glide reflection, distance is preserved.
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