Parallel Lines and Proportional Parts Section 6 4

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. 4 cm Parallel 8 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

Lesson Quiz: Part I Find the length of segment:

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