W. Gary Martin home page > CTSE 7970 > Write-up #3
CTSE 7970, Summer 2001, Write-up #3 – Why 1/7?
For this write-up, assume a working knowledge of high school geometry. Take a closer look at the following problem from Lab 5:
Triangle ABC is an arbitrary triangle. BD = (1/3)BC, CE = (1/3)CA, and AF = (1/3)AB. Triangle PQR is formed by the construction of line segments AD, BE, and CF. What is the relationship between triangle PQR and triangle ABC?
In class, we created a sketch that seemed to show that the triangle PQR is 1/7 of the area of triangle ABC. The question is, Is this really true? And if so, why is it true? The goal of this write-up is to gain as much insight as possible into this conjecture. You may find GSP a useful tool in better understanding what is happening in this situation.
Your write-up should include a statement of the conjecture; a description of your exploration, including any insights you gained; and (if possible) a proof. Even if you cannot complete the proof, report on the progress you made and what other findings you would need establish to finish the proof. The classroom implications should address how this sort of investigation might enhance your students' understanding of geometry and proof, along with any other suggestions you have for its use in the classroom.