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Geometric proof.

  1. Aug 24, 2010 #1
    Hello all, the picture i have attached is the question.
    http://img842.imageshack.us/img842/8921/geometricproof.png [Broken]


    I've concluded that there are two i isosceles triangles in this one triangle.

    [tex]\angle[/tex]PSQ + [tex]\angle[/tex]QSR = 90degrees
    Finding the angle in one of the isosceles triangles.

    [tex]\Delta[/tex]RQS with RQ = SQ
    RQ = SQ (given)
    If we put a line through the isosceles triangle and call this Z.
    RZ = SZ
    RZ = SZ (common to both)
    therefore: [tex]\Delta[/tex]RZQ =~ [tex]\Delta[/tex]SZQ
    therefore: [tex]\Delta[/tex]QRZ = [tex]\Delta[/tex]QSZ
    which results in: [tex]\angle[/tex]QRS = [tex]\angle[/tex]QSR
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 24, 2010 #2
    Hi,
    I dont understand your explanation on 'Z'!
    But your starting point is correct..You have two isosceles triangles (PSQ and QSR) in the triangle PSR.
    I will now give you a easy hint:
    First consider the isosceles triangle PSQ and find which two angles are equal?
    Then take the second isosceles triangle QSR and find which two angles are equal?
    Now you know the three angles of the triangle PSR = 180 degree.
    Got it!
     
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