Under Construction

Learning Focus

Use a compass and straightedge to copy segments, bisect angles and segments, and build equilateral triangles.

Big idea

A construction uses only a compass and straightedge. Key facts:

• A circle is all points at the same distance from its center.
• The perpendicular bisector of a segment is the set of points equidistant from its endpoints.
• An angle bisector splits an angle into two equal angles.

Worked example

Construct an equilateral triangle on $\overline{AB}$:

• Draw a circle centered at $A$ with radius $AB$.
• Draw a circle centered at $B$ with radius $AB$.
• Let $C$ be an intersection. Then $AC=AB=BC$.

If $AB=14$ and $M$ is its midpoint, $AM=7$. Bisecting an $80^\circ$ angle gives $40^\circ$.

Takeaways

• Compass radius keeps lengths equal.
• Intersecting arcs locate new points.
• Justify constructions with equal radii.