To duplicate a line segment AB, first draw a ray with point C by using a straightedge—this will be where the new line segment will be drawn. Measure the length of AB by using a compass. Then, keeping the compass at that length, use the straightedge and compass to draw a copy of AB. Move the compass to the endpoint of AB to draw a second copy of AB, keeping the straightedge in the same place. This line segment is now a distance of 2AB.
Once you know how to duplicate a line segment, you’re going to be asked to apply it in a lot of different ways. One way is to create 2AB. So you’re going to be given a line segment and you’re going to be asked to double it. Now you can’t just draw on a little more of this line segment and say, “Mr. McCall I’m done” you’re going to have to be very precise using your two tools of construction, a compass and a straight edge.
So we’re going to start by drawing a ray down below this line segment AB. You have to have a place to copy your new line segments onto. So I’m going to grab my straight edge and I’m going to draw a ray. So I’m going to duplicate 2AB onto this ray starting at point C.
So what I’m going to so is say, well 2AB, that’s just saying AB plus AB. So if I measure AB once I can copy it again and combining like terms AB and AB is 2AB. So I’m going to grab my compass and duplicating this line segment AB, I’m going to put a sharp end on one endpoint and I’m going to move my pencil, or for me a marker, until I have it exactly on the endpoint. So I’m not changing this at all.
I’m going to go down to point C and I’m going to make a mark. So this right here is 1AB so to make 2AB I’m going to put the sharp end on this new point and make another one. So notice that what I’ve done here is I’ve created a distance of 2AB. And I’m going to call this endpoint D.
So the key here was realizing that 2AB is just saying duplicate line segment AB twice.