Results 1 to 2 of 2

Thread: geometry angles the last

  1. #1
    Super Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    670
    Thanks
    4

    geometry angles the last

    ABC is a triangle
    |AB|=|ED|
    |BC|=|EC|
    Angle BAC=10
    find angle EDC=x?


    My work:
    I drew EK parallel to AB.
    I drew EB so EBD is isosceles.
    Angle ABE=a
    Angle EBD=b
    Angle AKD=a+b
    Angle CEK=10
    Angle BEK=a






    I extended AC and drew a line from B intersecting AC at
    F.Triangle BCF. Angle BCF=Angle ECD.BF=ED and BC=EC. I am
    sure triangles are congruent but I can't prove that.


    Attached Thumbnails Attached Thumbnails geometry angles the last-sexus.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2012
    From
    Istanbul
    Posts
    670
    Thanks
    4

    Re: geometry angles the last

    What do you think?
    Mark point F on AC extended, such that CF = CD. Then triangles BCF and
    ECD are congruent by SAS since BC = EC (given), CF = CD (by
    construction), and angle BCF = angle ECD (vertical angles). Therefore
    BF = ED (corresponding parts of congruent triangles), and since ED =
    AB (given), we see that BF = BA and triangle ABF is isosceles. Thus
    angle BAC = angle BFC = angle CDE, proving that angle CDE = angle BAC
    (which is 10 degrees).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Apr 5th 2017, 03:41 PM
  2. Geometry - Determine the angles
    Posted in the Geometry Forum
    Replies: 3
    Last Post: Oct 3rd 2009, 02:37 PM
  3. Geometry angles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Sep 18th 2008, 05:32 AM
  4. Geometry Angles
    Posted in the Geometry Forum
    Replies: 3
    Last Post: Sep 4th 2008, 05:32 PM
  5. geometry with angles
    Posted in the Geometry Forum
    Replies: 5
    Last Post: Sep 30th 2007, 07:20 PM

/mathhelpforum @mathhelpforum