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# 6.1: Perpendicular Bisector

Difficulty Level: At Grade Created by: CK-12

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?

Feb 23, 2012

Nov 03, 2014