lines are all parallel.Now we havelots of proportionalsegments.For example:
, , , , and manymore.This corollaryextendsto moreparallellines cuttingmoretransversals.
LinedNotebookPaperCorollary
Thinkabouta sheetof linednotebookpaper. A sheethas numerousequallyspacedhorizontalparallel
segments;theseare the linesa personcan writeon. And thereis a verticalsegmentrunningdownthe left
side of the sheet.This is the segmentsettingthe margin,so you don’twriteall the way to the edgeof the
paper.
Now supposewe drawa slantedsegmenton the sheetof linedpaper.
Becausethe verticalmarginsegmentis dividedinto congruentparts,then the slantedsegmentis also divided
into congruentsegments.This is the LinedNotebookPaperCorollary.
Whatwe’vedonehereis to dividethe slantedsegmentinto five congruentparts.By placingthe slanted
segmentdifferentlywe coulddivideit into any givennumberof congruentparts.