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Homework Help: Geometry Question

  1. Nov 22, 2011 #1
    Recently, I bought a book and found a strange question :

    In the given figure, PQRS is a quadrilateral. PO and QO are bisectors of angle P and angle Q respectively, then prove that angle QOP = 1/2 (angle R + angle S)

    I made several attempts to get the solution but failed. I guess, we need to prove that PQRS is a parallelogram.
     

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  2. jcsd
  3. Nov 22, 2011 #2

    ehild

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    Write out the sum of angles of the yellow pentagon.

    ehild
     

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  4. Nov 22, 2011 #3
    It's 540 degrees.
     
  5. Nov 22, 2011 #4

    ehild

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    OK. How is the angle a related to p/2 and q/2? What is the sum of angles of the pentagon in terms of a, p/2, q/2, r and s?

    ehild
     
    Last edited: Nov 22, 2011
  6. Nov 22, 2011 #5

    NascentOxygen

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    In triangle QOP, determine angle QOP, hence determine reflex angle QOP.
     
  7. Nov 26, 2011 #6

    ehild

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    Physics kiddy disappeared...

    p/2+q/2=180-a (triangle)
    p/2+q/2+r+s+360-a=540 (pentagon) -->

    180-a+r+s+360-a=540, 2a=r+s.

    ehild
     
  8. Nov 26, 2011 #7
    Thank you ! Thank you again. I disappeared because I found the solution in a book. But you wrote a completely new and easy method to solve this question. Now, I have got two ways to solve this question.
     
  9. Nov 26, 2011 #8

    ehild

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    I would like to see that solution from the book so much! Could you please show it?:smile:

    ehild
     
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