## Geometry – constructions 1 – copying segments

The constructions associated with copying a segment and copying an angle both require that you start your copy from a “location.” It is customary to start by drawing a straight line from which to copy. A “reference line” is a line like this.
Proof of Construction: The compass was used to determine (and copy) the length of the specified segment. The segments are congruent since the given segment and the copy are the same length.
6. Position the compass point on the starting point (dot) on the reference line and swing an arc that intersects the reference line and goes above the reference line without increasing the size of the compass.
7. Return to the specified angle ABC and calculate the arc’s span (width) from where it crosses one side of the angle to where it crosses the other. (Draw a tiny arc to indicate how far you measured.)
Evidence of Construction: Once the construction is complete, draw line segments connecting the points where the first arcs intersect the angles’ sides. Since they reflect the measured stretches of the same arcs, we know these lengths are the same in both drawings. These segments will be combined to form two triangles with three sets of congruent (equal) sides. We know that ABC is congruent to A’B’C’ since the triangles are congruent by SSS and any remaining corresponding sections would be congruent (by CPCTC).

## Copy a line segment

These linesegments are currently in separate rows but in the same table, and the numbers in the picture represent the ids of the respective linestrings. I’d like to copy linesegments 350, 333, 352,4,… in one table and 1601, 1602,356, 576,580,344,… in another. In terms of algebra, set A members are in one table and set B members are in another, even if there is a visual intersection. This is a representative sample, and these sets contain more ids than those mentioned here, as well as more sets than the two A and B described here. Is it possible to do this with PostGIS queries or a Python script?

### How to copy a line segment – geometric constructions

To duplicate a line segment AB, begin by drawing a ray with point C using a straightedge; this will be the starting point for the new line segment. Using a compass, determine the duration of AB. Then, holding the compass at that length, draw a copy of AB with the straightedge and compass. Draw a second copy of AB by shifting the compass to the endpoint of AB and holding the straightedge in the same place. This line segment is now 2AB in length.
You’ll be asked to repeat a line segment in a variety of ways once you’ve learned how to do it. One choice is to make 2AB. So you’ll be given a line segment and instructed to double it. You can’t just add a little more to this line section and say, “Mr. McCall, I’m done,” because you’ll need to be very accurate with your two construction instruments, a compass and a straight edge. So, to begin, we’ll draw a ray down below this line segment AB. You’ll need a spot to paste your new line segments. So I’m going to take out my straight edge and draw a ray. So, beginning at point C, I’ll replicate 2AB onto this ray. So what I’m going to do is say 2AB, which is simply AB plus AB. So, if I calculate AB once, I can copy it again, and 2AB is formed by combining the words AB and AB. So I’ll take my compass and duplicate this line section AB, putting a sharp end on one endpoint and moving my pencil, or in my case, a marker, until it’s exactly on the endpoint. But I’m not going to change anything. I’m going to go down to point C and make a label there. So this is 1AB, so I’m going to place the sharp end on this new point and make another one to make 2AB. So you’ll find that I’ve built a distance of 2AB. I’m going to refer to this as endpoint D. The key was to realize that 2AB simply means “duplicate line segment AB twice.”

### Duplicating a line segment

geometric building / house / geometry / form

### How to copy a line segment using straightedge and compass

Geometrical form

### Segment copy construction

Geometric construction is the method of drawing lines, angles, and other geometric shapes and figures using only a compass and a straightedge (typically a ruler without measurements) and no precise length, angle, or other measurements.
To draw circles and arcs, a natural or mechanical compass, such as the one shown above, is used. It’s even possible to copy line segments with it. The right-hand straightedge or ruler is for drawing line segments, not for measuring length.
Place the point end of the compass at a point, O, and the pencil end of the compass at point A to draw a circle or arc. Then, to make arc AB, move the pencil end counterclockwise to point B. Continue drawing an arc until the compass’s pencil end makes a full circle back to point A to draw a complete circle. The circle’s radii are represented by the line segments OA and OB.