1. Constructions Centoids

2. Review of Prerquisite To construct a perpendicular bisector you need a... Fish. Let’s begin !

3. A Median is a segment connecting the vertex of a triangle to the opposite midpoint. Medians

4. The medians of a triangle are concurrent at a point called the centroid.

6. Construction of the Median Start with the FISH to find a midpoint of side BC. Start with the base and point B.

7. Construct arc from point B past the midpoint of BC

8. Construct arc from point C past the midpoint of BC Connect the arc intersection points to find the midpoint. Construct the median from A to the midpoint.

9. Construction of the Median from C

10. Construct arc from point B past the midpoint of BA

11. Construct arc from point A past the midpoint of BA Connect the arc intersection points to find the midpoint. Construct the median from C to the midpoint.

12. Centroid It is not necessary to construct all three medians because… Two intersecting lines determine a point.

13. It is only necessary to draw 2 medians. The third median would only intersect the other lines at the same point. We will now look at several examples of centroids to solidify your understanding.

14. 1 4 3 2

15. Let’s try another centroid construction.

16. Construction of the Median Start with the FISH to find a midpoint of side BC. Start with the base and point B.

17. Construct arc from point B past the midpoint of BC

18. Construct arc from point C past the midpoint of BC Connect the arc intersection points to find the midpoint. Construct the median from A to the midpoint.

19. Construct arc from point B past the midpoint of BA

20. Construct arc from point A past the midpoint of BA Connect the arc intersection points to find the midpoint. Construct the median from C to the midpoint.

21. Centroid It is not necessary to construct all three medians because… Two intersecting lines determine a point.

22. When two medians intersect then they divide each other into a small segment and a large segment. Let’s look at several situations.

27. The ratio is always 2:1 Therefore… If DF = 5, then AD = _____ 5 10 ?

28. If DF = 5, then AD = _____ 10 7 ?

29. If AD = 12, then DF = _____ 12 ? 6

30. If AD = 16, then DF = _____ 16 ? 8

31. Summary 2. The three medians of a triangle are concurrent. 1. A Median is a segment connecting the vertex of a triangle to the opposite midpoint. 3. The point of concurrency is called a centroid.

32. Summary 4. When two medians intersect then they divide each other into a large segment and a small segment.

33. Summary 5. The centroid is always inside the triangle. 6. To construct the median you… You construct a fish on 2 sides. You connect the opposite vertex to the midpoint.

34. C’est fini. Good day and good luck. A Senior Citizen Production That’s all folks.