Copy a Segment

Our first construction is the easiest:

Given segment AB, construct another segment CD that is congruent to AB: 

 

The way to do it is to make a circle with radius AB and center C, choose any point on the circumference as point D, and then draw the segment CD. 

First set the compass:  place the point of the compass at point A and set it so the pencil is on point B.  This way you measure the correct radius.  Then use the straight-edge to draw a line (rather, a segment) that is clearly longer than AB.  Label point C on the left of the line and place the point of the compass there.  Finally, sweep out an arc that intersects the line.  The point of intersection is point D:

Use the compass to "measure" AB:

Place the point at C and sweep out an arc of a circle of radius AB:

Here is an animation of this process.

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