Constructing the Midpoint and the Perpendicular Bisector of a Segment
Try it Yourself...
Verify with GeoGebra
Draw the segments and in the app above or on paper, then use the GeoGebra tools or a ruler to measure their lengths. Which polygon do you obtain?
Describe the properties of the obtained polygon, examining in particular the relationships between the lengths of the sides, the measures of the angles and the mutual position of the diagonals.
Based on your considerations above, explain why is the midpoint of .
When constructing the midpoint and the perpendicular bisector, we have drawn the two circles centered at the endpoints of the segment and radii equal to the segment's length. In your opinion, is the choice of the radius length unique? If it is not unique, explain what is the minimum compass opening (relative to the segment's length) that allows you to graphically obtain the midpoint and the perpendicular bisector of the segment.
Explain why the segment is perpendicular to .
Find the missing word in the following sentence: Since the segment is perpendicular to and passes through its midpoint, we can say that the line is the ______________________ of segment .