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5.1­5.2 Midsegments & Perpendicular Bisectors                        November 02, 2012

                                                        5.1 
                                                           Midsegment of a Triang
     Midsegment of a Triangle: 
                       segment that connects the midpoints of 2 sides of a 
                               Every triangle has 3 midsegments.




     Midsegement Theorem:
                   midsegment is parallel to the 3 side and is 1/2 as long

                                    B
                                                  DE // AC
                           D            E         DE = 1/2 AC
                    A                        C              DF // BC
                                F                           DF = 1/2 BC
                                                                          EF // BA
                                                                          EF = 1/2 BA




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                                                             5.2 
                                                                Perpendicular Bisector
     Equidistant: 
              same distance
     Perpendicular Bisector:
                      a segment that is perpendicular to a segment at its midpoint.
                     C
             A           P      B       CP is   bisesctor of AB

   Perpendicular Bisector Theorem: If a point is on the    bisector, then it is equidistant from 
                    C                the endpoints of the segment. 

                                        If CP is      bisesctor of AB, then CA = CB
              A          P      B

    Converse of the Perpendicular Bisector Theorem: If a point in equidistant from the 
                                                        endpoints of a segment, then it is 
                             C                          on the    bisector.
                      A        P      B If DA = DB, then D lies on the   bisesctor of AB.


                                    D




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    Concurrent:
              when 3 or more lines intersect in the same point
    Point of Concurrency:
                     the point of intersection




    Circumcenter:
             the point of concurrency of the 3 perpendicular bisectors of a 




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5.1­5.2 Midsegments & Perpendicular Bisectors          November 02, 2012




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5.1 5.2 notes