9 6 proportional parts and parallel lines

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  1. Proportional Parts and Parallel LinesProportional Parts and Parallel LinesYou will learn to identify and use the relationships betweenparallel lines and…
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  • 1. Proportional Parts and Parallel LinesProportional Parts and Parallel LinesYou will learn to identify and use the relationships betweenparallel lines and proportional parts.Nothing New!
  • 2. Proportional Parts and Parallel LinesProportional Parts and Parallel LinesOn your given paper,draw two (transversals)lines intersecting the parallel lines.CDEFABLabel the intersections of thetransversals and the parallel lines,as shown here.Measure AB, BC, DE, and EF.,Calculate each set of ratios:BCABEFDEACABDFDE,Do the parallel lines divide the transversals proportionally? Yes
  • 3. Proportional Parts and Parallel LinesProportional Parts and Parallel LinesTheorem 9-8If three or more parallel lines intersect two transversals,the lines divide the transversals proportionally.lmnBAC FEDIf l || m || nACBCDFEF=ThenBCABEFDE= ,ACABDFDE= and,
  • 4. Proportional Parts and Parallel LinesProportional Parts and Parallel LinesabcHGJ WVU1812x15Find the value of x.HJGHVWUV=1812x15=12x = 18(15)12x = 270x = 2221
  • 5. Proportional Parts and Parallel LinesProportional Parts and Parallel LinesTheorem 9-9If three or more parallel lines cut off congruent segments onone transversal, then they cut off congruent segments onevery transversal.lmnBAC FEDIf l || m || n andThenAB  BC,DE  EF.
  • 6. Proportional Parts and Parallel LinesProportional Parts and Parallel Lines(x +3)10(2x – 2)10Find the value of x.F(x + 3) = (2x – 2)x + 3 = 2x – 25 = xTheorem 9 - 98 8EDCBADE  EFSince AB  BC,
  • 7. Proportional Parts and Parallel LinesProportional Parts and Parallel Lines
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