Proving Theorems about Lines and Angles

Perpendicular Bisectors

This activity will help you meet these educational goals:

• Mathematical PracticesYou will make sense of problems and solve them, reason abstractly, and look for regularity in repeated reasoning.
• InquiryYou will perform an investigation in which you will make observations, make hypotheses, analyze results, and communicate your results in written form.

Directions

Read the instructions for this self-checked activity.Type in your response to each question, and check your answers.

Activity

In this activity, you will use GeoGebra to find a relationship between a perpendicular bisector and the line segment it bisects.Openperpendicular bisectors, and complete each step below.

Copy and paste in browser. Perpendicular Bisector

http://contentstore.ple.platoweb.com/content/GeoGebra.v5.0/A2.5_Perpendicular_Bisector.html

Question 1

In the diagram,CDis perpendicular toAB.CreateAC

andBC, and measure their lengths.How do the lengths compare?

Diagram is referring to the diagram that is opened with link listed above

Question 2

Slide pointCalong the perpendicular bisector so the lengths ofACandBC increase or decrease.Does the relationship between the lengths ofACandBCchange?If so, how?

Question 3

CreateADandBD, and measure their lengths.How do the lengths compare?How is the relationship between the lengths ofAD

andBDaffected if pointDis moved along the perpendicular bisector?

Question 4

Finally, place a new point anywhere on the screen, but not on the perpendicular bisector.Label the pointF. CreateAF

andBFusing the new point.What do you notice about the lengths ofAFandBF?

Now select pointF, and move it around the screen.Where must you locate pointFsoAF=BF?Explain.