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# Constructions

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1. Constructions Centoids

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

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

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

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

6. 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.

7. Construction of the Median from C

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

9. 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.

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

11. 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.

12. 1 3 2 4

13. Let’s try another centroid construction.

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

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

16. 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.

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

18. 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.

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

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

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

22. 10 If DF = 5, then AD = _____ ? 7

23. 6 If AD = 12, then DF = _____ 12 ?

24. 8 If AD = 16, then DF = _____ 16 ?

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

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

27. 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.

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