This lab leads you to discover properties of medians of a triangle and compare different points of concurrency with each other.

Part1[br]1. CD, AE and BF are all medians of triangle ABC. Drag points A, B and C. Do the medians ever intersect outside of the triangle?[br]2. Click on “Show lengths of segments AE, AG and GE”[br]3. Calculate the ratio of AG/AE: _______________[br]4. Calculate the ratio of GE/AE: _______________[br]5. Unclick “Show lengths of segments AE, AG and GE” then click on “Show lengths of segments DC, CG and DG.”[br]6. Calculate the ratio of GC/DC: _______________[br]7. Calculate the ratio of DG/DC: _______________[br]8. Unclick “Show lengths of segments DC, CG and DG” then click on “Show lengths of FB, GB and FG.”[br]9. Calculate the ratio of GB/FB: _______________[br]10. Calculate the ratio of FG/FB: _______________[br]11. The medians all meet at a point called the centroid. Write a conclusion about where the centroid is in respect to the length of the medians.[br]Part 2[br]12. Unclick everything from Part 1. Click on “Show Perpendicular Bisectors.”[br]13. What do the perpendicular bisectors and medians have in common?[br]14. How are perpendicular bisectors and medians different?[br]15. Why do you think there’s a circle around the triangle with the perpendicular bisectors?[br]16. Unclick “Show Perpendicular Bisectors” then click on “Show Angle Bisectors.”[br]17. What do angle bisectors and medians have in common?[br]18. How are angle bisectors and medians different?[br]19. Why is there a circle inside of the triangle with angle bisectors?[br]20. When are the points of concurrency the same?[br]21. Write a conclusion for this lab.