An Exploration of
Triangle Concurrency

This exploration uses Key Curriculum's Geometer's Sketchpad as the principal dynamic geometry tool. These pages require access to the software GeometerŐs Sketchpad and a web browser capable of supporting the graphics. The files can be adapted to work for Cabri Geometry by downloading the html files and making some minor changes in the code and then creating the companion sketches in Cabri to replace the *.gsp and *.gss files. We have included a number of built in interactive sketches and have also added answers to questions posed in the investigations sections.

Your students will be better able to move through this material if they are familar with these topics.

• Acute, obtuse, scalene, isosceles, equilateral and right triangles.
• Angle bisector, perpendicular bisector, altitude and median.
• Basic geometric construction skills, compass and straightedge sketches.

They will also benefit from some prior exposure to the Geometer's Sketchpad and a web browser. These apecific computer skills will help their journey the the web go smoothly.

• Previous experience creating sketches with the Geometer's Sketchpad
  Construction and text tools.
  The basic commands on the File, Edit, Display and Construct Menus.
  the ability to play simple Scripts.
• Time spent navigating the web using a browser,
  Especially using the Back Button or Back Arrow to get back to a previous page.
  The ability to switch between applications on a computer (Sometimes the web page will cover up the sketch you are working on. You need to be able to get the sketch back on top so you can continue your work.)
  Ability to print or save sketches with and without text added to them.

We have included periodic teacher checkpoints throughout the material, but have been purposefuly vague on the specific "teacher directed activites." This will require that you decide in advance how you want to collect data and record their investigations. We have deliberately left out instructions to students about assessment issues. We felt that each teacher has their own system, so we have included reminders to check with the teacher about specfic requirements. Some of the systems that could be used with these materials are...

• Students maintain a hoomework disk to recors their sketches and the answers to investigation questions.
• Students work through the material interactively with no work turned in. Accountability is established through a test or a writing assignment.
• Students work through the material, answer investigation questions on a worksheet and print important sketches.
• Students put their names and answers to investigation questions in a textbox on the sketch and print or save them.

If you have any questions or comments you can reach us via email at...