Integrated Math 1 / Unit 9: Coordinate Geometry and Constructions
9.5 Basic Constructions
Notes
A construction uses only a compass and a straightedge (an unmarked ruler). The compass copies lengths and draws arcs.
- Copy a segment: draw a ray, set the compass to the segment's length, and mark off that length on the ray.
- Bisect a segment (perpendicular bisector): with the compass wider than half the segment, draw arcs from both endpoints that cross above and below; draw a line through the two crossings.
- Bisect an angle: draw an arc across both rays from the vertex; from each crossing, draw arcs of equal radius that meet inside the angle; draw a ray from the vertex through that meeting point.
- Keep the compass setting unchanged when a step says "same radius."
Practice
To construct the perpendicular bisector of segment $AB$, which step is correct?
Arcs from both endpoints with equal radius over half of $AB$ cross at two points that lie on the perpendicular bisector.
To copy a segment $AB$ onto a ray, what should you do with the compass?
The compass transfers the distance between $A$ and $B$.
A construction bisects an $80^\circ$ angle. What are the measures of the two new angles?
Bisecting splits an angle into two equal angles: $80^\circ \div 2 = 40^\circ$.
Ready for more? Take the Unit 9 test.