Straightedge — Definition, Formula & Examples
A straightedge is an unmarked straight tool used to draw lines through two points. Unlike a ruler, it has no measurement markings — its only job is to create perfectly straight lines.
In classical Euclidean construction, a straightedge is an idealized instrument of infinite length and no markings that permits exactly one operation: drawing the unique line (or line segment) determined by any two given points.
How It Works
You place the straightedge so its edge passes through two known points, then draw a line along it. Because it has no markings, you cannot use it to measure or transfer distances. To perform most geometric constructions, you pair the straightedge with a compass — the compass handles distances and circles, while the straightedge handles straight lines. Together, these two tools let you bisect angles, construct perpendicular lines, copy segments, and much more.
Example
Problem: Using a straightedge and compass, construct the perpendicular bisector of a segment AB.
Step 1: Open the compass to any radius greater than half of AB. Place the compass point on A and draw an arc above and below the segment.
Step 2: Without changing the compass width, place the point on B and draw arcs that intersect the first pair. Label the intersection points P and Q.
Step 3: Use the straightedge to draw a line through P and Q. This line is the perpendicular bisector of AB — it crosses AB at its midpoint at a 90° angle.
Answer: The line through P and Q, drawn with the straightedge, is the perpendicular bisector of AB.
Why It Matters
Straightedge-and-compass constructions form the backbone of classical geometry, a topic central to middle and high school math courses. Understanding these constraints also connects to famous unsolved-then-proven problems, like the impossibility of trisecting an arbitrary angle with these tools alone.
Common Mistakes
Mistake: Using the edge of a ruler and reading its markings to measure distances during a construction.
Correction: A straightedge has no markings. If a problem says 'straightedge and compass construction,' you may not measure lengths — only draw lines through points and arcs with the compass.