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What kind of line crosses another line?

If you learn how to construct special types of lines, you'll be able to solve problems involving lines even if a picture of the lines is not given to you. One line that you've seen in this lesson but not identified by name is the perpendicular bisector. You already know what perpendicular means, but what about bisector

You have probably used words like bicycle and biannual, knowing that the prefix bi- means two. You may or may not know that the word sector means part--usually, equal parts. If you put the parts of the word together, you get a word that means two equal parts, or two halves. A perpendicular bisector is a line that intersects a segment at a right angle, cutting it into two equal halves. The point of intersection is the line segment's midpoint.

Which line is a bisector in the diagram below? Click the image when you think you know.

Question

How can you use drawing tools to construct a bisector?

First, use a straightedge to draw a line and mark a point on the line. Then use your compass to construct two points that are equidistant from the first point. Using your compass, construct a point that when connected to the first point, will form a line perpendicular to the original line.

In other words, draw perpendicular lines, and make sure the transversal crosses the first segment at its midpoint.