LESSON 6.2 PROPERTIES OF PARALLELOGRAMS

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LESSON 6.2 PROPERTIES OF PARALLELOGRAMS Powered By Docstoc
					               LESSON 6.2
    PROPERTIES OF PARALLELOGRAMS


    OBJECTIVE:
    Use relationships among sides and
    among angles of parallelograms

    Use relationships involving diagonals
    or parallelograms and transversals
              Slide Courtesy of Miss Fisher
1                   Modified 1/28/08
                    Definitions
      Check for Understanding: Starting with Ð K move
     counterclockwise around   JKLM to name pairs of
     consecutive angles.


    Consecutive angles of a polygon
        share a common side.
        ____________________




    In   JKLM, ÐJ and ÐM are consecutive
    angles, as are ÐJ and Ð___. ÐJ and Ð___
                                  K      L
         opposite Courtesy angles.
    are ____________ of Miss Fisher
                 Slide
2                      Modified 1/28/08
                    Theorems
      Check for Understanding: If RT and US bisect one
     another at point M, name two pairs of @ segments.


    Theorem 6.1
         ___________ sides of a parallelogram are @.
          Opposite

    Theorem 6.2
                                                 @
         Opposite angles of a parallelogram are ____.

    Theorem 6.3
                                            bisect
         The diagonals of a parallelogram _________
         each other.
                   Slide Courtesy of Miss Fisher
3                        Modified 1/28/08
                 Theorems Con’t

    Theorem 6.4

    If three (or more) parallel lines cut off
    congruent segments on one transversal,
    then _____________________________
           they cut off congruent segments
    _________________________________
    on every transversal.


          BD @ DF
         _________

                Slide Courtesy of Miss Fisher
4                     Modified 1/28/08
    EXAMPLE #1
    Find the value of x in       ABCD.
    Then find mÐA.


     Opposite angles of a                     mÐB = x + 15
     parallelogram are congruent
                       _________                    = 60 + 15
                                                    = 75°
     so, x + 15 = 135 - x
        2x + 15 = 135                   *mÐA + mÐB = 180
             2x = 120                     mÐA + 75 = 180
              x = 60                           mÐA = 105°
     *Recall, consecutive angles in a parallelogram are
                     Slide Courtesy of Miss Fisher
5    supplementary, since __________________________.
                             // lines à same-side int. Ðs supp.
                           Modified 1/28/08
    EXAMPLE #2

     Find the values of x
     and y in    KLMN.

                                   bisect
    Diagonals of a parallelogram ______ each other,
    so Substitute 7y -16 for x in the second equation.
       x = 7y – 16              and             2x + 5 = 5y
       x = 7(3) – 16                    2(7y – 16) + 5 = 5y
       x = 21 – 16                         14y – 32 + 5 = 5y
       x=5                                         14y – 27 = 5y
                                                        -27 = -9y
      Substitute 3 for y in the first                     3=y
                     Slide Courtesy of Miss Fisher
6     equation.             Modified 1/28/08
    EXAMPLE #3
    In the figure DH || CG || BF || AE,
    Find EH.

    If three (or more) parallel lines cut off congruent
    segments on one transversal, then
    _________________________________
     they cut off congruent segments on every
    _________________________________
     transversal, so EF = FG = GH.

     EH = EF + FG + GH
     EH = 2.5 + 2.5 + 2.5
     EH = 7.5 units
                    Slide Courtesy of Miss Fisher
7                         Modified 1/28/08
    Assignment: pg 297 #2-16, even,
    17, 19, 22, 34-35, 39-41




             Slide Courtesy of Miss Fisher
8                  Modified 1/28/08

				
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