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This activity is intended to supplement Geometry, Chapter 5, Lesson 2.

Problem 1 – Exploring the Perpendicular Bisector Theorem

Start the Cabri Jr. application by pressing APPS and selecting CabriJr. Open the file PERBIS by pressing Y=, selecting Open..., and selecting the file.

Line CD is the perpendicular bisector of \overline{AB}. Find AC and BC using the Distance and Length tool (press GRAPH and select Measure > D.&Length). Remember that AC means the length of \overline{AC}.

1. Move point C to 4 different positions and record the measurements in the table below. To move the point, move the cursor over the point, press a, move the point to the desired location, and then press a again to release the point.

Position 1^{st} position 2^{nd} position 3^{rd} position 4^{th} position
AC
BC

2. What is the relationship between the measurements of AC and BC?

3. Make a conjecture based on your results above about a point on the perpendicular bisector and the endpoints of a segment.

Problem 2 – An Application of the Perpendicular Bisector Theorem

John and Jane are a young college graduate couple who are relocating to a new city. They have jobs at separate locations, but work out at the same gym. They would like to buy a house that is equidistant from their jobs and gym. They use the map below and see that John’s workplace is located at B7, Jane’s workplace is at J6, and their gym is located at E3.

Open the Cabri Jr. file POINTS. Three points are plotted: ordered pair (1, 3.5) represents B7; ordered pair (5, 3) represents J6; and ordered pair (2.5, 1.5) represents E3.

  1. Use Perpendicular Bisector Theorem to decide where John and Jane should live.
  2. Using the map’s notation, where should the young couple live?

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