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A line of symmetry, , is a line separating a figure into two halves that are mirror images.
Line symmetry exists for a figure if for every point P on one side of the line, there is a corresponding point Q where is the perpendicular bisector of .
Line of Symmetry
Figures can be reflected through lines of symmetry onto themselves.
Lines of symmetry determine the amount of rotation required to carry them onto themselves.
Not all figures are symmetrical.
Regular polygons have sides of equal length and angles of equal measure. There are n number of lines of symmetry for a number of sides, n, in a regular polygon.
Example: Squares
Because squares have four equal sides and four equal angles, squares have four lines of symmetry.
Rotating a square about its center 90
If we rotate a square about its center 90, we find that though the points have moved, the square is still covering the same space.
Similarly, we can rotate a square 180, 270, or any other multiple of 90 with the same result.
Practice # 1
Given a regular pentagon ABCDE, draw the lines of symmetry.
Continue around to each vertex, extending a line from the vertex to the midpoint of the opposing line segment.
Note that a regular pentagon has five sides, five vertices, and five lines of reflection.
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