If point A' is the mirror image of point A in a figure with a line of symmetry, then the line of symmetry is the perpendicular bisector of the segment AA'.
You can use that fact to reflect figures over lines without using a device like a Mira. Suppose you 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.
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