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Understanding Proportional Parts and Similar Triangles

This resource explores key concepts surrounding similar triangles and their properties. It discusses the Proportional Parts Conjecture, which states that in similar triangles, the lengths of altitudes, medians, and angle bisectors are proportional to the corresponding sides. Additionally, it covers the Angle Bisector Theorem, demonstrating how a triangle's angle bisector divides the opposite side into segments that are proportional to the adjacent sides. These principles are crucial for solving related geometric problems.

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Understanding Proportional Parts and Similar Triangles

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  1. 4/28/2014

  2. 11.44/28 Corresponding Parts of Similar Triangles p. 52 Proportional Parts Conjecture If 2 triangles are similar, then the lengths of the following are proportional to the corresponding sides: Altitudes Medians Angles bisectors

  3. Angle Bisectors

  4. p. 52L Angle Bisector/Opposite Sides Conjecture A bisector of an angle in a triangle divides the opposite side into 2 segments whose lengths are in the same ratio as the lengths of the 2 sides forming the angle.

  5. Practice

  6. 4/29/2014

  7. HW Qs? 16.5 22 11 17.1

  8. 8.4 18 17.3 8.4

  9. 11.74/29 Proportional Segments/Parallel Lines p. 53

  10. p. 53L Extended Parallel/Prop.Conjecture If 2 or more lines are parallel to the side of a triangle, then the sides are divided proportionally.

  11. p. 67L

  12. 4/30/2014

  13. H6: p. 627 #1-11

  14. 5/1/2014

  15. 5/2/2014

  16. HW Qs? 7. Yes, QRSP ~ XYZW, SF = 2.5 8. X = 1.5 9. X = 7 10. AA, LMN ~ PQN, x = 9 11. 24.5 12. W = 32, x = 24, y = 40, z = 126 D B B B A Yes, AA, ABC ~ DEF, SF=1.5

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