
Let's quickly review what we already know about reflections
and how the preimage and image are positioned in relation to one another.
An object and its reflection have the same shape and size, but the figures face in opposite directions, appearing as mirror images.
The reflection line, m, is the perpendicular bisector of the segments joining each point to its image.
The existence of the perpendicular bisector will be the reflection's connection to constructions. Let's see how we can put it to work. 
If you need additional information on reflections,
go to the section on Transformations.

Given a figure and its reflection, construct the line of reflection.
Given: ΔD'E'F' is the reflection of ΔDEF
in some line in the same plane.
Task: Construct the line of reflection

Connect any vertex of ΔDEF to its image
(E to E'). Construct the perpendicular bisector of the segment formed. Done.

This example chose to connect E to E'. You could, however, have chosen to connect D to D' or F to F' for your construction.
It is sufficient to choose only one set of corresponding points to get the line of reflection. You need not bisect all three connected segments, unless you want to test the accuracy of your construction. 

Given a figure and line of reflection, construct the reflected image.
Given: ΔABC and reflection line n in the same plane.
Task: Construct the reflected image of ΔABC and label it ΔA'B'C'

Choose a starting vertex (A). Construct a perpendicular from A to the line of reflection. Measure the length from A to the intersection point. Copy this length on the perpendicular bisector starting at the intersection point to find A'.
You have located ONE vertex of the image.

After repeating this process for each of the three vertices, you will have the vertices of the image ΔA'B'C'. Done.
The order in which you repeat this process is of no importance. 

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