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5.4 – Use Medians and Altitudes

5.4 – Use Medians and Altitudes. Line from the vertex of a triangle to the midpoint of the opposite side. Line from the vertex of a triangle perpendicular to the opposite side.

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5.4 – Use Medians and Altitudes

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  1. 5.4 – Use Medians and Altitudes

  2. Line from the vertex of a triangle to the midpoint of the opposite side Line from the vertex of a triangle perpendicular to the opposite side

  3. Construct a triangle with the given sides. Then construct the median for each side of the triangle. What do you notice? B A A C B C

  4. C A B

  5. C A B

  6. Line from the vertex to midpoint of opposite side

  7. 2/3 the distance from each vertex and 1/3 distance from the midpoint Centroid

  8. Construct a triangle with the given sides. Then construct the perpendicular bisector for each side of the triangle. What do you notice? B A A C B C

  9. C A B

  10. C A B

  11. Line from vertex  to the opposite side

  12. orthocenter If acute – inside of triangle If obtuse – outside of triangle If right – at vertex of right angle

  13. C P I A C M O A

  14. 6

  15. In PQR,S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure. Find TP. 3

  16. In PQR,S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure. Find SV. 3 2

  17. In PQR,S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure. Find RU. 3 2 4 + 2 = 6 4

  18. In PQR,S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure. Find ST. 3 3 2 4

  19. In PQR,S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure. Find VQ. 3 3 2 4 5

  20. In ABC,G is the centroid, AE = 12, DC = 15. Find the measure. B Find GE and AG. GE = 4 AG = 8 E D 12 G A C F

  21. In ABC,G is the centroid, AE = 12, DC = 15. Find the measure. B Find GC and DG. GC = 10 DG = 5 E D 12 G 15 A C F

  22. Point L is the centroid for NOM. Use the given information to find the value of x. OL = 5x – 1 and LQ = 4x – 5 5x – 1 2(4x – 5) 5x – 1 = 4x – 5 5x – 1 = 8x – 10 –1 = 3x – 10 9 = 3x 3 = x

  23. Point L is the centroid for NOM. Use the given information to find the value of x. LP = 2x + 4 and NP = 9x + 6 9x + 6 3(2x + 4) = 6x + 12 = 9x + 6 9x + 6 12 = 3x + 6 2x + 4 6 = 3x 2 = x

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