# Medians of a triangle

- Author:
- Rachel Fruin

- Topic:
- Median Line, Special Points, Triangles

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

Part1
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?
2. Click on “Show lengths of segments AE, AG and GE”
3. Calculate the ratio of AG/AE: _______________
4. Calculate the ratio of GE/AE: _______________
5. Unclick “Show lengths of segments AE, AG and GE” then click on “Show lengths of segments DC, CG and DG.”
6. Calculate the ratio of GC/DC: _______________
7. Calculate the ratio of DG/DC: _______________
8. Unclick “Show lengths of segments DC, CG and DG” then click on “Show lengths of FB, GB and FG.”
9. Calculate the ratio of GB/FB: _______________
10. Calculate the ratio of FG/FB: _______________
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.
Part 2
12. Unclick everything from Part 1. Click on “Show Perpendicular Bisectors.”
13. What do the perpendicular bisectors and medians have in common?
14. How are perpendicular bisectors and medians different?
15. Why do you think there’s a circle around the triangle with the perpendicular bisectors?
16. Unclick “Show Perpendicular Bisectors” then click on “Show Angle Bisectors.”
17. What do angle bisectors and medians have in common?
18. How are angle bisectors and medians different?
19. Why is there a circle inside of the triangle with angle bisectors?
20. When are the points of concurrency the same?
21. Write a conclusion for this lab.