Math 487 Autumn 2002 - Lab 2: Distance and Perpendicular Bisectors

This lab uses explorations in Geometry Through the Circle. Write your responses to the Answer in Writing parts on the Lab Report 2 form.

1. Demo of trace of circles through 2 points. Relation with perpendicular bisector.

2. Carry out Exp. 3.2, Inv. 1: Two Ripples.

Answer in writing: Q1, Q2, Q3, Q4.

3. Carry out Exp 3.2, Inv 2: Three Ripples. (Skip the Explore more for now.)

Answer in writing: Q2. You will be asked to prove Q1 later.

4. Carry Out Exp 3.3, Inv 1: Perpendicular Bisectors in a Triangle. (Skip for now the Script and the Explore Mores.)

Answer in writing: Q1 and Q2.

5. Carry Out Exp 3.3, Inv 2: Perpendicular Bisectors of Chords.

Answer in writing: Q1 (give a proof) and Q2.

6. Read the text in the box: Conclusions – Locus Property. Notice that you have already proved both statements in your homework.

Definition: A collection of 3 or more lines is concurrent when all the lines pass through a single point.

Answer in writing: Prove that for any triangle ABC, the perpendicular bisectors of the side are concurrent at a point O.

Answer in writing: The point O is called the circumcenter of ABC. Explain why for any triangle ABC, there is exactly one circle that passes through A, B and C; and the circle is centered at O.

Tools and Investigations

Follow directions to make a Circumcircle Tool.

• Use the Circumcircle Tool to investigate Explore More – Corner Circles of Exp 3.3.
• Use the Circumcircle Tool to investigate Challenges – Inscribing Kites of Exp 3.3.