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Constructions PowerPoint Presentation
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Constructions

Constructions

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Constructions

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Presentation Transcript

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

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

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

  7. 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.

  8. Construction of the Median from C

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

  10. 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.

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

  12. 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.

  13. 1 3 2 4

  14. Let’s try another centroid construction.

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

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

  17. 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.

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

  19. 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.

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

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

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

  23. 10 If DF = 5, then AD = _____ ? 7

  24. 6 If AD = 12, then DF = _____ 12 ?

  25. 8 If AD = 16, then DF = _____ 16 ?

  26. 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.

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

  28. 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.

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