Using Coordinate 
   Geometry to Prove 
   Parallelograms
   • Definition of Parallelogram
   • Both Pairs of Opposite Sides Congruent
   • One Pair of Opposite Sides  Both Parallel and Congruent
   • Diagonals Bisect Each Other
   L34 Opener
   QUAD JOHN J(-3,1) O(3,3)  H(5,7)  N(-1,5)
   a)  Use the slope formula and calculate the slope of all 
   four sides.
   b) Write down and fill in the blanks
   Segments with the same slopes are _____.  Since opposite 
   sides are _____ then QUAD JOHN is a _______ by the
   _______________.  
   c) Graph QUAD JOHN and check that it is a parallelogram.
      Definition of a Parallelogram
    Use Coordinate Geometry to show that quadrilateral 
    ABCD is a parallelogram given the vertices A(0, 0 ),
    B(2, 6), C (5, 7) and D(3,1) .                       B           C
               I need to show that both 
                pairs of opposite sides                 A         D
                are parallel by showing 
                  that their slopes are 
                          equal.
      Definition of a Parallelogram
    Use Coordinate Geometry to show that quadrilateral 
    ABCD is a parallelogram given the vertices A(0, 0 ),
    B(2, 6), C (5, 7) and D(3,1) .                       B           C
     AB: m = 6 – 0  =  6  = 3
                   2 – 0       2  AB ll  CD             A         D
     CD: m = 1 – 7   =  - 6  = 3                   ABCD is a 
                    3 – 5       - 2
     BC: m = 7 – 6  =  1                           Parallelogram
                    5 – 2      3                    by Definition
     AD: m = 1 – 0  = 1           BC  ll  AD
                    3 – 0     3
 Both Pairs of Opposite 
 Sides Congruent
   Use Coordinate Geometry to show that quadrilateral 
   ABCD is a parallelogram given the vertices A(0, 0 ),
   B(2, 6), C (5, 7) and D(3,1) .
                                B     C
       I need to show that both 
        pairs of opposite sides 
                               A     D
        are congruent by using 
        the distance formula to 
         find their lengths.