How exactly do you draw a perpendicular bisector without the use of measuring tools? Remember, geometric constructions must be done with only a compass and a straight edge – no measuring allowed. A perpendicular bisector is a line that passes through the midpoint of another line segment at ninety degrees. It cuts the line segment in half. So how are you supposed to draw this line without measuring the angle with a protractor, or finding the center of the segment without a ruler? Let me show you.

First, we will start with a line segment, and expand your compass so that it is wider than half the length of the line segment. Your compass might look like this one, or completely different, but all geometric compasses are similar in that they draw circles, or parts of circles called an arc, but fixing one end of the compass in place, and allowing the other end of the compass to swing around on the page. Up next in our construction, we need to fix one end of the compass at one end of the segment, and then strike an arc above and below the segment. You could draw the entire circle like this, but you don't need to, only two arcs from this circle are needed. The next step is really important. WITHOUT CHANGING THE WIDTH OF THE COMPASS, strike another pair of arcs from the other endpoint of the segment. If done correctly, you should see two sets of intersecting arcs. Mark these intersections with points. Finally, connect these points with your straight edge.

There you have it. You constructed a perpendicular line exactly through the middle of the original segment without the use of any measuring tools. You should watch this video again, and practice the steps until you can create a perpendicular bisector on your own.

Good luck!