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In Session 5, you saw three ways to move figures around: rotation, reflection, and translation. If you can move an entire design in one of these ways, and that design appears unchanged, then the design is symmetric.
If you 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 you 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:
The dashed lines below are not lines of symmetry. Though they do cut the figures in half, they don't create mirror-image halves.
You can use a Mira (image reflector) or simply the process of cutting and folding to find lines of symmetry. Print the PDF version of the figures above, and compare the lines proposed using a Mira.
In Problems A1 and A2, sketch the figures or print the PDF files of the figures and show the lines of symmetry as dashed lines.
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