text: # Homework Help: Geometric proof.
  
  1. Aug 24, 2010
  
  ### Sirsh
  
  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.
  
  $$\angle$$PSQ + $$\angle$$QSR = 90degrees
  Finding the angle in one of the isosceles triangles.
  
  $$\Delta$$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: $$\Delta$$RZQ =~ $$\Delta$$SZQ
  therefore: $$\Delta$$QRZ = $$\Delta$$QSZ
  which results in: $$\angle$$QRS = $$\angle$$QSR
  
  Last edited by a moderator: May 4, 2017
  2. Aug 24, 2010
  
  ### Rajini
  
  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!
explanation: The document is a homework help request for a geometric proof. It contains a question about proving a geometric property of a triangle and an attempt at solving the problem. The user provides a detailed explanation of their approach, and another user offers a hint to guide the solution.
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distilabel_metadata.role: system
distilabel_metadata.content: # Homework Help: Geometric proof.
  
  1. Aug 24, 2010
  
  ### Sirsh
  
  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.
  
  $$\angle$$PSQ + $$\angle$$QSR = 90degrees
  Finding the angle in one of the isosceles triangles.
  
  $$\Delta$$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: $$\Delta$$RZQ =~ $$\Delta$$SZQ
  therefore: $$\Delta$$QRZ = $$\Delta$$QSZ
  which results in: $$\angle$$QRS = $$\angle$$QSR
  
  Last edited by a moderator: May 4, 2017
  2. Aug 24, 2010
  
  ### Rajini
  
  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!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a homework help request for a geometric proof. It contains a question about proving a geometric property of a triangle and an attempt at solving the problem. The user provides a detailed explanation of their approach, and another user offers a hint to guide the solution. 
  
  Label: question-and-answer