Geometry / Unit 1: Foundations of Geometry
1.6 Basic Constructions
Notes
A construction is a drawing made with only a compass and a straightedge (a ruler with no marks).
- A compass copies distances. A straightedge draws lines.
- To copy a segment, set the compass to its length and mark that length on a ray.
- The perpendicular bisector of $\overline{AB}$: draw arcs of equal radius (more than half of $AB$) from $A$ and $B$; join the two crossing points.
- To bisect an angle: draw an arc from the vertex across both sides, then equal arcs from those two points; join the vertex to where they cross.
- Every point on the perpendicular bisector of $\overline{AB}$ is the same distance from $A$ and $B$.
Practice
Which tools are allowed in a classic geometric construction?
Constructions use only a compass and an unmarked straightedge.
Point $P$ lies on the perpendicular bisector of $\overline{AB}$, and $PA = 9$. What is $PB$?
Points on a perpendicular bisector are equidistant from the endpoints.
When constructing a perpendicular bisector of $\overline{AB}$, the compass must be set to:
If the radius is half or less, the arcs do not cross in two points. The same width is used from both ends.
Ready for more? Take the Unit 1 test.