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Parallel Lines and Proportional Parts

Parallel Lines and Proportional Parts. Section 6-4. Proportional Parts of Triangles:. Non-Parallel transversals that intersect 2 Parallel lines can be extended to form 2 similar triangles. Line a ║line b. Line a. Line b. Example: Finding the Length of a Segment. Find US.

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Parallel Lines and Proportional Parts

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  1. Parallel Lines andProportional Parts Section 6-4

  2. Proportional Parts of Triangles: • Non-Parallel transversals that intersect 2 Parallel lines can be extended to form 2 similar triangles. Line a║line b Line a Line b

  3. Example: Finding the Length of a Segment Find US. Since segment ST║segment UV, then ∆RST ~ ∆RUV.

  4. Example: Find PN. PN = 7.5

  5. Verify that . Since , by the Converse of the Triangle Proportionality Theorem. Example: Verifying Segments are Parallel

  6. AC = 36 cm, and BC = 27 cm. Verify that . Since , by the Converse of the Triangle Proportionality Theorem. Example:

  7. Midsegment in a Triangle: • Segment whose endpoints are the midpoints of 2 sides of a triangle. Triangle Midsegment Theorem: A midsegment of a triangle is║to one side and its length is half that side. 4 cm Parallel 8 cm

  8. Triangle Midsegment Theorem Corollaries: • If three or more║lines intersect two transversals, then they cut off the transversals proportionally. • If three or more║lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

  9. If lines AD, BE, and CF are ║, then: • AB/BC = DE/EF • AC/DF = BC/EF • AC/BC = DF/EF

  10. If lines AD, BE, and CF are ║ and AB  BC, then DE  EF

  11. Lesson Quiz: Part I Find the length of segment:

  12. Verify that BE and CD are parallel. Since , by the Converse of the ∆Proportionality Thm. Lesson Quiz: Part II

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