OTHER USEFUL
C O N S T R U C T I O N S
Copying line segments is another vital skill needed for constructions. Here is the basic instruction on how to copy line segments.
Given segment AB, construct a segment CD, so that AB=CD.
Step 1. Measure the lenght of AB using your compass.
Step 2. Draw an arc centered at point C. Connect C with any point D on the arc. CD will equal AB.
Constructing perpendicular lines.
You may already know how to construct a perpendicular bisector to a line. What about a perpendicular line through any point?
Given line AB and point C, construct a line perpendicular to AB through point C.
Step 1. Draw a circle at C so that it intersects AB at two points, D and E.
Step 2. Find the perpendicular bisector of DE. This line is the the perpendicular to AB.
Constructing parallel lines. Given line AB, construct a line at C parallel to AB. Basically, just construct a perpendicular line through C. Then construct another line perpendicular to that line, through C.
Another easy way of drawing parallel lines is using what I call, the "Quadrant" method. Select two points on line AB. Construct two circles of equal radius at those points. Draw a line tangent to both circles at their quadrant.
Copying angles
Given angle ABC, construct an angle at vertex P equal to angle ABC.
First, at point B draw a circle of any radius, intersecting at D and E. Draw a circle with the same radius as BE at point P, calling the intersection R. Draw an arc at point E, with radius ED.
Draw a circle at point R with the radius ED. Circle R intersects circle P at Q. Connect points P and Q. Angle QPR=ABC.
| Square | Triangle and Hexagon | Pentagon | Golden Ratio | Nonagon |
| Pentadecagon | Heptadecagon | N-Gon | Squaring a Circle | Heptagon |
