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. Since segment ST║segment UV, then ∆RST ~ ∆RUV.

Example: Find PN. PN = 7.5

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

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

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. Parallel 8 cm 4 cm

Triangle Midsegment Theorem Corollaries: 1.If three or more ║ lines intersect two transversals, then they cut off the transversals proportionally. 2.If three or more ║ lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

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

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

Find the length of segment: Lesson Quiz: Part I

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