IM2.6.3 Proving Conjectures
Construction Task
1. Recreate the construction above (the labels on your points can be different letters than mine, but it might get a little confusing later…). Lines JK, FI, and GH are parallel.[br][br]Then answer the questions below
2. List the similar triangles in your construction.
3. Tristan wrote the proportion [math]\frac{EJ}{JF}=\frac{EK}{KI}[/math] based on this diagram, but Tia thinks he’swrong. “Some of those segments aren’t even sides of triangles!” Make segments,[br]read the measurements, and calculate the proportions to test Tristan’s[br]conjecture. Who is right?
4. Write as many different proportions as you can, testingthem as you go. Make sure you use some segments that don’t have E as an[br]endpoint.