Symmetry is one of the most important ideas in mathematics. In this session, we will explore geometric versions of symmetry by creating designs and examining their properties.
If we can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or Line symmetry. The line that we reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror- image halves. The dashed lines below are Lines of symmetry.
(Reflection is a rigid motion, meaning an object changes its position but not its size or shape. In a reflection, one can create a mirror image of the object. There is line that acts like the mirror. In reflection, the object changes its orientation (top and bottom, left and right). Depending on the location of the mirror line, the object may also change location)
The dashed lines below are not lines of symmetry. Though they do cut the figures in half, they don’t create mirror image halves.
For each figure, find all the lines of symmetry you can.
Solution:
Find all the lines of symmetry to these regular polygons. Generalize a rule about the number of lines of symmetry for regular polygons.
Perpendicular Bisector
Suppose we want to reflect the triangle below over the line shown. To reflect point A, draw a segment from A perpendicular to the line. Continue the segment past the line until you’ve doubled its length. You now have point A’, the mirror image of A.
Repeat the process for the other two endpoints and connect them to form the triangle.
Reflect the following figure using the concept of perpendicular bisector.
Solution:
