Results 1 to 2 of 2

Math Help - isosceles trapezoid

  1. #1
    Junior Member
    Joined
    Jun 2007
    Posts
    60

    isosceles trapezoid

    Could someone please help me prove that this is an isosceles trapezoid? Thank you in advance.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    645
    Hello, sanee66!

    In quadrilateral MNOA, triangles PNO and PMA are congruent
    and APO is an isosceles triangle.
    Prove that MNOA is an isosceles triangle.
    Code:
                          P
              M * - - - - * - - - - * N
               /     β  *   *  β     \
              /      *        *       \
             /    *              *     \
            /   *                   *   \
           / *  α                   α  * \
        A * - - - - - - - - - - - - - - - * O

    Since \Delta PNO \cong \Delta PMA\!:\;MA = NO
    . . So we must prove that: . MN \parallel AO

    Since \Delta PNO \cong \Delta PMA\!:\;\angle MPA = \angle NPO
    . . Let \angle MPA = \angle NOP = \beta

    We note that: . 2\beta + \angle APO \:=\:180^o .[1]


    Since \Delta APO is isosceles, \angle PAO = \angle POA
    . . Let \angle PAO = \angle POA = \alpha

    In \Delta APO\!:\;2\alpha + \angle APO \:=\:180^o\quad\Rightarrow\quad \angle APO \:=\:180^o -2\alpha

    Substitute into [1]: . 2\beta + (180^o -2\alpha) \:=\:180^o\quad\Rightarrow\quad \alpha = \beta

    Hence: . MN \parallel AO .(alternate-interior angles)

    Therefore, MNOA is an isosceles trapezoid.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Isosceles trapezoid problem
    Posted in the Geometry Forum
    Replies: 36
    Last Post: December 15th 2010, 08:40 AM
  2. [SOLVED] isosceles trapezoid
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 24th 2010, 11:10 PM
  3. isosceles trapezoid help
    Posted in the Geometry Forum
    Replies: 3
    Last Post: November 2nd 2009, 05:10 PM
  4. Area of Isosceles Trapezoid
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 3rd 2009, 04:44 PM
  5. Area of an Isosceles Trapezoid
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: December 4th 2007, 06:52 AM

Search Tags


/mathhelpforum @mathhelpforum