Bisect a Segment

Today we’ll be doing a very simple construction — bisecting a segment.  In other words, we will be cutting a line segment in half.  Begin by drawing matching circles from your two endpoints (A and B).  The radius of the circle is not important.  As long as it is more than half the length of your segment, it will work.

Call the points where these two matching circles cross C and D.  Use a straight edge to connect C to D.

°

In addition to cutting segment AB in half, this construction does a few other bits of math magic.  Segments AB and CD are perpendicular to each other, so we’ve also constructed four 90° angles, and depending on how you look at it, a pair of reflected congruent right triangles or an isosceles triangle.  That isosceles triangle can be reflected over segment AB by connecting A and B to point D, forming a charming little rhombus.