5. RelationshipsWithinTriangles...................................................................................................
Midsegmentsof a triangle
LearningObjectives
- Identifythe midsegmentof a triangle.
- Applythe MidsegmentTheoremto solveproblemsinvolvingside lengthsand midsegmentsof triangles.
- Use the MidsegmentTheoremto solveproblemsinvolvingvariableside lengthsand midsegmentsof
triangles.
Introduction
In previouslessons,we usedthe parallelpostulateto learnnew theoremsthat enabledus to solvea variety
of problemsaboutparallellines:
ParallelPostulate:Given:line and a point not on. Thereis exactlyone line
through that is parallelto.In this lessonwe extendtheseresultsto learnaboutspecialline segmentswithintriangles.For example,
the followingtrianglecontainssucha configuration:
Triangle is cut by where and are midpointsof sides and respectively.
is calleda midsegment of. Notethat has othermidsegmentsin additionto. Can you see wherethey are in the figureabove?
If we constructthe midpointof side at point and construct and respectively, we have
the followingfigureand see that segments and are midsegmentsof.