Right tri sim day 1

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Right tri sim day 1

  1. 1. GT Geometry Drill 3/7/14 Turn in HW on the bookshelf What is the geometric mean of the two measurements?
  2. 2. GT Geometry Drill 3/7/14 Turn in HW on the bookshelf What is the geometric mean of the two measurements? 1) 2 and 8 2) 16 and 1 3) 12 and 2
  3. 3. Objective •Students will explore the properties of similar right triangles so that they can find unknown sides.
  4. 4. Altitude to Hypotenuse
  5. 5. Altitude to Hypotenuse
  6. 6. Altitude to Hypotenuse • The altitude extending from the hypotenuse to the right angle.
  7. 7. 21 hh b a 1 d e 2 c
  8. 8. Example c a d b
  9. 9. Example d d c a c c b a d b
  10. 10. Example c a d b
  11. 11. Example d d c a c c b a d b
  12. 12. Example c a d b
  13. 13. Example d d c a c c b a d b
  14. 14. Example c a d b
  15. 15. Example d d c a c c b a d b
  16. 16. Example c a d b
  17. 17. Example d d c a c c b a d b
  18. 18. Example c a d b
  19. 19. Example d d c a c c b a d b
  20. 20. Right ∆ Similarity Theorem • The altitude to the hypotenuse of a right triangle divides the triangle into 2 triangles that are similar to each other and the original triangle.
  21. 21. Solve for x x 6 3
  22. 22. Solve for x x 8 4
  23. 23. Corollary 1 • The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.
  24. 24. • d h = h e h d e
  25. 25. •Long-Long, Short-Short d h = h e h d e
  26. 26. • Long-Long, Short-Short • The ratio of the longer legs is equal to the ratio of the d h shorter legs = h h d e e
  27. 27. •Solve for x: 9 5 x
  28. 28. Example x 5 5=x x 8 8 x=?
  29. 29. Corollary 2 • The altitude to the hypotenuse of a right triangle intersects it so that the length of each leg is the geometric mean of the length of its adjacent segment of the hypotenuse and the length of the entire hypotenuse.
  30. 30. Example h d b e d+e=b b e
  31. 31. Example x 3 2 1 3 +1 = 2 2 1
  32. 32. Classwork •Assignment #78
  33. 33. Conclusion • 1) A right triangle can be divided by its altitude so that… • 2) In your own words, state what Long-Long, ShortShort means.

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