6.1: Perpendicular Bisector
This activity is intended to supplement Geometry, Chapter 5, Lesson 2.
ID: 11198
Time required: 15 minutes
Activity Overview
In this activity, students will explore the perpendicular bisector theorem and discover that if a point is on the perpendicular bisector of a segment, then the point is equidistant from the endpoints. This is an introductory activity where students will need to know how to grab and move points, measure lengths, and construct the perpendicular bisector with Cabri Jr.
Topic: Triangles & Their Centers
- Perpendicular Bisector Theorem
Teacher Preparation and Notes
- This activity was written to be explored with the Cabri Jr. on the TI-84.
- To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
- To download the calculator files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=11198 and select PERPBIS and POINTS.
Associated Materials
- Student Worksheet: Perpendicular Bisectors http://www.ck12.org/flexr/chapter/9690
- Cabri Jr. Application
- PERPBIS.8xv and POINTS.8xv
In this activity students will explore the properties of perpendicular bisectors. In the first part, students will measure the distance to a point on the bisector to identify congruent segments. In the second part, students will apply what they have learned about perpendicular bisectors to the context of map coordinates.
Problem 1 – Exploring the Perpendicular Bisector Theorem
Students will be exploring the distance from a point on the perpendicular bisector to the endpoints of a segment and discover that if a point is on the perpendicular bisector of a segment, then it is equidistant from the two endpoints of the segment.
Students will measure the lengths of segments using the Distance & Length tool (press GRAPH and select Measure > D.&Length). To drag a point, students will move the cursor over the point, press ALPHA, move the point to the desired location, and then press ALPHA again to release the point.
Problem 2 – An Application of the Perpendicular Bisector Theorem
Students will apply what they learned from problem one and find the intersection of two perpendicular bisectors to find a point equidistant from three points.
To draw a segment, students should use the Segment tool (press WINDOW and select Segment). To draw a perpendicular bisector, press ZOOM and select Perp. Bis..
Solutions
Problem 1 – Exploring the Perpendicular Bisector Theorem
- Answers will vary. The measures of \begin{align*}\overline{AC}\end{align*}
AC¯¯¯¯¯¯¯¯ and \begin{align*}\overline{BC}\end{align*} should be equal. - Sample answer: \begin{align*}AC\end{align*} is congruent to \begin{align*}BC\end{align*}. The distances are the same.
- If a point is on the perpendicular bisector of a segment, then it is equidistant from the two endpoints of the segment.
Problem 2 – An Application of the Perpendicular Bisector Theorem
- (6, 7)
- \begin{align*}F7\end{align*}