Noticethat thereare pointswherethe perpendicularsegmentintersectsboth parallellines.It intersectsthetop line at and the bottomline at You needto find the lengthof this segment,and you know
two points.You can use the distanceformulawhichyou learnedin algebraand whichwe brieflyreviewed
in Chapter1. Substitutethe - and -coordinatesfrom thesepointsinto the formula,and you’llhavethe
distancebetweenthe two parallellines.
The distancebetweenthe two lines is , or about units.LessonSummary
In this lesson,we exploredperpendiculartransversals.Specifically, we havelearned:
- How to identifythe implicationsof perpendiculartransversalson parallellines.
- How to identifythe conversetheoremsinvolvingperpendiculartransversalsand parallellines.
- To understandand use the distancebetweenparallellines.
Thesewill help you solvemanydifferenttypesof problems.Alwaysbe on the lookoutfor new and interesting
waysto applythe conceptsof perpendiculartransversalsto new mathematicalsituations.
Pointsto Consider
Findingthe distancefrom a pointto a line and the distancebetweentwo linesare two goodexamplesof
waysto applyskillsyou learnedin algebra,suchas findingslopesand usingthe distanceformulato geom-
etry problems.Evenwhengeometricproblemsare givenwithouta coordinatesystem,you can oftendefine