Results 1 to 4 of 4

Math Help - Proving the congruency of two triangles in a parallelogram.

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    4

    Smile Proving the congruency of two triangles in a parallelogram.

    ABCD is a parallelogram and P is a point on the diagonal AC. Prove that triangle ABP and APD have the same area.
    How do I prove this?
    The attachment is a picture of a parallelogram that is drawn. Please use theorem to prove this, thank you.
    Whoever solve this will save my life.
    Attached Thumbnails Attached Thumbnails Proving the congruency of two triangles in a parallelogram.-screen-shot-2010-11-21-1.11.59-am.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,811
    Thanks
    116
    Quote Originally Posted by RoyJones View Post
    ABCD is a parallelogram and P is a point on the diagonal AC. Prove that triangle ABP and APD have the same area.
    How do I prove this?
    The attachment is a picture of a parallelogram that is drawn. Please use theorem to prove this, thank you.
    Whoever solve this will save my life.
    1. The diagonal AC divides the parallelogram into 2 congruent triangles. Since these two triangles have the same base (= AC) the distances of the parallels to the diagonal must be equal.

    2. Therefore the triangles APB and ADP have the same height and the same base AP. Thus the areas must be equal.
    Attached Thumbnails Attached Thumbnails Proving the congruency of two triangles in a parallelogram.-parallelogramm_teilfl.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Great solution!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    888
    Thanks
    25
    Quote Originally Posted by Also sprach Zarathustra View Post
    Great solution!
    How simple it is when you know the fundamentals.Thanks earboth
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving parallelogram (vectors)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 8th 2010, 12:06 PM
  2. Proving a Quadrilateral is a parallelogram
    Posted in the Geometry Forum
    Replies: 1
    Last Post: November 28th 2008, 09:11 PM
  3. Replies: 2
    Last Post: May 8th 2008, 04:18 PM
  4. Proving Congruency
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 20th 2008, 05:45 PM
  5. Geometry - Triangles - Congruency
    Posted in the Geometry Forum
    Replies: 6
    Last Post: May 28th 2007, 05:39 AM

Search Tags


/mathhelpforum @mathhelpforum