The definition and properties of the perpendicular bisector are explored using a geometry applet.
The perpendicular bisector of a line segment AB is a line that is perpendicular to AB and passes through the midpoint of segment AB.(see figure below).
To construct a perpendicular bisector, we may proceed as follows:
1 - draw two circles centered at A and B and with equal radii.
2 - connect the intersections P and Q of the two circles to make a line. This line is perpendicular to AB and passes through the midpoint M of segment AB.(see figure below).
A large screen applet is used to explore the definition and properties of the perpendicular bisector.
1 - click on the button above "click here to start" and MAXIMIZE the window obtained.
2 - Click continuously on the button "increase radius" left panel. For each radius the intersections (2 points) of the circles are plotted as red points. The locus of these points is the perpendicular bisector.
3 - Click on the button "draw bisector on/off" to draw the perpendicular bisector.
4 - Click continuously on the button "increase radius" and you will notice that the two points of intersection of the two circles are on the perpendicular bisector.
5 - Explore
a- Segments PA and PB are congruent because they are radii of circles with equal radii. Segments QA and QB are also congruent. Explain why triangles APQ and BPQ are congruent.
b - Show that triangles APM and BPM are congruent.
b - Show that the line through PQ satisfies the definition of the perpendicular bisector given above.