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Medians & Altitudes

Medians & Altitudes. The intersection of the medians is called the CENTROID. Theorem 5.8 The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint. 2x. x. C. How much is CX?. D. E. X. 13. B. A. F. C.

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Medians & Altitudes

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  1. Medians & Altitudes

  2. The intersection of the medians is called the CENTROID.

  3. Theorem 5.8 The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint. 2x x

  4. C How much is CX? D E X 13 B A F

  5. C How much is XD? D E X 18 B A F

  6. Ex: 1 In ABC, AN, BP, and CM are medians. C If EM = 3, find EC. N P E B M A

  7. Ex: 2 In ABC, AN, BP, and CM are medians. C If EN = 12, find AN. N P E B M A

  8. C N P E B M A Ex: 3 In ABC, AN, BP, and CM are medians. If CM = 3x + 6, and CE = x + 12, what is x?

  9. Altitude Altitude vertex to opposite side and perpendicular

  10. The intersection of the altitudes is called the ORTHOCENTER.

  11. Tell whether each red segment is an altitude of the triangle. The altitude is the “true height” of the triangle. YES NO YES

  12. Perpendicular Bisector and Angle Bisector

  13. 5-2 Perpendicular Bisector perpendicular to a side at its midpoint

  14. 5-2 Perpendicular Bisector Theorem If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

  15. The intersection of the perpendicular bisector is called the CIRCUMCENTER.

  16. What is special about the CIRCUMCENTER? Equidistant to the vertices of the triangle.

  17. Point G is the circumcenter of the triangle. Find CG. Example 2: A E D G 6 B 8 C F 10

  18. 5-3 Angle Bisector Angle Bisector cuts the angle into 2 equal parts

  19. The intersection of the angle bisectors is called the INCENTER.

  20. What is special about the INCENTER? Equidistant to sides of the triangle

  21. Point G is the incenter of the triangle. Find GB. Example 1: A 7 E D G 5 2 B C F 7

  22. Example 1: Point N is the incenter of the triangle. Find the length of segment ON. 18 30

  23. Example 2: Point N is the incenter of the triangle. Find the length of segment NP.

  24. Homework • p. 266 #13-18 • 275 #14-17 • p. 280 #1-6, 10-14 Learn your vocabulary!!!

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