Exercises 1-3 below are to be performed in GeoGebra. Exercises 4 and 5 are to be answered using complete sentences, including precise mathematical terminology. Email your completed homework to kpoirier@citytech.cuny.edu by 2:30pm on Thursday, October 13.

Exercises 1-3 are to be completed in GeoGebra. If you are using the desktop version of GeoGebra, attach your files to your email. If you are using the web-browser version of GeoGebra, include a link to your worksheet in the email.

Your answers for exercises 4 and 5 can be written in the body of your email, attached as a separate document, or included as text boxes in your GeoGebra file.

 

  1. Construct a triangle \bigtriangleup ABC. Construct the centroid, orthocenter, and circumcenter. Label these points G, H, and O, respectively.
  2. Put a line through two of the points constructed above. What relationship do you notice among the three points. Use the drag test to see if this relationship continues to hold. Add your conclusion as a text box in your GeoGebra worksheet.
  3. Measure the distances HG and GO. Describe the ratio $latex \frac{HG}{GO} as the triangle changes. Add this ratio as a text box in your GeoGebra worksheet.
  4. Write a clear summary of the relationships among the triangle centers that you discovered above (these relationships are the Euler Line Theorem).
  5. Does the above activity constitute a proof of the Euler Line Theorem? Why or why not?