So, eachpersonwill travelfive milesto meetat the midpointbetweenNandi’s and Arshad’s houses.SegmentBisectors
Now that you knowhow to find midpointsof line segments,you can exploresegmentbisectors.A bisector
is a line, segment,or ray that passesthrougha midpointof anothersegment.You probablyknowthat the
prefix“bi” meanstwo (thinkaboutthe two wheelsof abicycle).So, a bisectorcuts a line segmentinto two
congruentparts.
Example 3
Use a ruler to drawa bisectorof the segmentbelow.The first step in identifyinga bisectoris findingthe midpoint.Measurethe line segmentto find that it is 4
cm long.To find the midpoint,dividethis distanceby 2.
So, the midpointwill be 2 cm from eitherendpointon the segment.Measure2 cm from an endpointand
drawthe midpoint.
To completethe problem,drawa line segmentthat passesthroughthe midpoint.It doesn’tmatterwhat
anglethis segmenttravelson. As long as it passesthroughthe midpoint,it is a bisector.
CongruentAngles
You alreadyknowthat congruentline segmentshaveexactlythe samelength.You can also applythe
conceptof congruenceto othergeometricfigures.Whenanglesare congruent,they haveexactlythe same
measure.Theymay pointin differentdirections,havedifferentside lengths,havedifferentnamesor other
attributes,but their measureswill be equal.
NotationNotes:1.Whenwritingthat two anglesare congruent,we use the congruentsymbol: Alter-
natively, the symbol refers to the measure of , so we could write
and that has the samemeaningas. You may notice
then,thatnumbers(suchas measurements)are equalwhileobjects(suchas anglesand segments)
are congruent.- Whendrawingcongruentangles,you use an arc in the middleof the angleto showthat two anglesare
congruent.If two differentpairsof anglesare congruent,use one set of arcs for one pair, then two for
the next pair and so on.