Results 1 to 2 of 2

Math Help - a triangle geometry...

  1. #1
    Member
    Joined
    Feb 2010
    From
    in the 4th dimension....
    Posts
    122
    Thanks
    9

    a triangle geometry...

    let in triangle ABC,AB=AC. D is the midpoint of BC.E is the foot of the perpendicular from D to AB,and F is the midpoint of DE.
    Prove that AF is perpendicular to CE.

    please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
    This is a problem of USSR MO , i have solved it already .


    Let  M be the mid-pt of  BE , from  BD = CD we have  CE \parallel DM .

    Then consider that  \Delta ADE \sim \Delta DBE so

     \Delta AFD \sim \Delta DMB because  F is the mid-pt of DE while  M is the mid-pt of  BE

    We can find that  AF is perpendicular to  DM .

    ( Median perpendicular to median as sides perpendicular to sides , check it ! )


    Therefore ,  CE is perpendicular to  AF as  CE \parallel DM mentioned before .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Geometry triangle help?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 29th 2008, 04:45 AM
  2. triangle geometry
    Posted in the Geometry Forum
    Replies: 4
    Last Post: November 17th 2008, 12:29 PM
  3. Replies: 1
    Last Post: November 15th 2007, 02:01 AM
  4. geometry triangle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 15th 2007, 06:30 PM
  5. Triangle Geometry
    Posted in the Geometry Forum
    Replies: 2
    Last Post: January 4th 2006, 09:20 AM

Search Tags


/mathhelpforum @mathhelpforum