CK12 - Geometry

Note:FigureNOTto scale

Are lines and parallel?

First,noticethat the diagramis labeled“not to scale.”Do not makeyour decisionbasedon how this diagram

looks.Rememberthat if one angleat an intersectionmeasures all four anglesmeasure Fill in
the anglemeasuresyou can identifywith this information.

Sincethe correspondinganglesare all thesetwo linesare parallel.The transversalis perpendicular

to both lines and , so they mustbe parallel.

DistanceBetweenParallelLines

Whenwe talk aboutthe distancebetweentwo points,whatwe are reallytalkingaboutis the shortestor
mostdirectdistancebetweenthosetwo points.On paper, you can use a ruleror a taut stringto find the
distancebetweentwo points.Whenyou measurethe distancebetweena line and a point,the mostdirect
path from a pointto a line is alwaysmeasuredalongthe perpendicularfrom the pointto the line.

Similarly, sometimesyou mightbe askedto find the distancebetweentwo parallellines.Whenyou needto
find this value,you needto find the lengthof a perpendicularsegmentthat connectsthe two lines.Remember
that if a line is perpendicularto one parallelline, it is perpendicularto both of them.Let’s look at an example
on a coordinategrid.

Example 3

Whatis the distancebetweenthe two lines shownon the grid below?