-?capm@Ϫoϫ38 .?+8aACBT v{ .?+8aBBC< JO .?+8aCCdB .?+8aDC[C=    .?+8a +[Fr A midsegment in a triangle connecting midpoints of two sides is parallel to the third side and half its measure. The diagonals of a quadrilateral divide it into four triangles BDC, DCA, CAB, and ABD. Therefore, the midsegments of ACD and ABD are congruent and parallel, because they are parallel to the same diagonal. For the same reason, the midsegments of CAB and BDC are also congruent and parallel. Therefore, the connection of the midsegments forms a parallelogram. This is true for any quadrilateral.ilateral.._cV  .?+8aP9SnAly Theeman, 13, Grade 8 Jessica Rosenblatt, 13, Grade 8 Claire Gross, 13, Grade 8 Julie Pancoe, 13, Grade 8 Ashok Surapaneni, 13, Grade 7 Garland St. Middle School, Bangor, Maine December Problem of the Month..//002u  .?+8ajKKK(|CBTBC<?2O  .?+8akCBTCdB?u  .?+8alBC<C[C=?ID  .?+8amC[C=CdB?Iu  .?+8arBC<CdB?2  .?+8asCBTC[C=??D .?+8aEC4B  .?+8aFC_C w}| .?+8aGBB  .?+8aHC)C< m!  .?+8am13 x  m {S:BC} = PϨ2ϥ~Ϥϧϧz  8 <V+P aPLength(Segment BC) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\ nE4 .?+8am14  m {S:AD} = PϨ2ϥ~Ϥϧϧz  8 <V+P aPLength(Segment AD) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\ >||  .?+8anBBC4B? >  .?+8aoC4BC_C?   .?+8apC_CC)C<?v|  .?+8aqC)C<BB?k wQ .?+8am9 JJ0 J(  m{!:A}GHF = PϨ2ϥ~Ϥϧϧz  8 <V+P aP Angle(GHF) = t AD) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\x V .?+8am10  m{!:A}HFE = PϨ2ϥ~Ϥϧϧz  8 <V+P aP Angle(HFE) = t AD) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\ P .?+8am11  m{!:A}FEG = PϨ2ϥ~Ϥϧϧz  8 <V+P aP Angle(FEG) = t AD) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\  W .?+8am12  m{!:A}EGH = PϨ2ϥ~Ϥϧϧz  8 <V+P aP Angle(EGH) = t AD) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\ 3 @l .?+8am5  m {S:GE} = PϨ2ϥ~Ϥϧϧz  8 <V+P aPLength(Segment GE) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\A Nk .?+8am6  m {S:EF} = PϨ2ϥ~Ϥϧϧz  8 <V+P aPLength(Segment EF) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\O \l .?+8am7  m {S:FH} = PϨ2ϥ~Ϥϧϧz  8 <V+P aPLength(Segment FH) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\] jm .?+8am8  m {S:HG} = PϨ2ϥ~Ϥϧϧz  8 <V+P aPLength(Segment HG) = @@ ,$@9l u@P@@ Ϩ2hϩh@ @Č@ >~ >L@eN 9ϦxϦhϨϨtϩh  ( axx2h -).@@ -).+8@@+ϤϤϤhϥ6&Ϧ@4@6@6@p \  -  HH\