# Perpendicular Bisector Theorem (Part 1)

- Author:
- Tim Brzezinski

The applet below contains a segment (with endpoints A & B) and a point P that is equidistant from this segment's endpoints.

Instructions:
1) Notice how point C (in green) is the same distance (equidistant) from points A and B.
In fact,Point C has been programmed to always be EQUIDISTANT from the black segment's endpoints.
Use your mouse to drag point C around show show the locus (set of points) on your computer screen
that are equidistant from A and B.
2) What does this locus (set of points) look like? Explain.
3) Now, move point A and/or point B to change the position and length of the segment.
Then, click on the house button in the toolbar shown on the upper right hand side of the applet.
(This house button says "Back to Default View" and will erase all traces of green dots you've already made.)
4) Repeat steps (1) and (2) again, this time for this "newer" segment with endpoints A and B.
4) Click on checkbox (A) to show the locus (set of points) on your computer screen that are
EQUIDISTANT from A and B.
5) Use your observations to fill in each ( ) with the correct word to make a true statement:
This set of points (shown in step 4 above) looks like it is the ( ) ( ) of segment AB.
6) Click checkboxes (B) and (C) in the applet above to either check your answer to step (5) or help you fill in the
( )'s for step (5).
7) Use your observations above to fill in each blank below to make a true statement:

**“If a point is ( ) from the ( ) of a segment, then that point must lie on the ( ) ( ) of that segment.”**