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Math Help - Quadrilateral identity

  1. #1
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    Quadrilateral identity

    In a convex quadrilateral ABCD, AB=BC+DA. Bisectors of ABC and BAD meet at P. Show that CP=DP.
    Sadly, no ideas on this one.
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  2. #2
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    Quote Originally Posted by atreyyu View Post
    In a convex quadrilateral ABCD, AB=BC+DA. Bisectors of ABC and BAD meet at P. Show that CP=DP.
    Sadly, no ideas on this one.
    1. I assume that you mean the angle bisector ... ? (Drawn in blue) If so:

    2. Draw a sketch (see attachment)

    3. For symmetry reasons the 2 orange segments must be as long as the red segment.
    Attached Thumbnails Attached Thumbnails Quadrilateral identity-gleiche_entferng.png  
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