1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     

    Attached Files:

  2. jcsd
  3. Nov 22, 2011 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Write out the sum of angles of the yellow pentagon.

    ehild
     

    Attached Files:

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

    ehild

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar

    Staff: Mentor

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

    ehild

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

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

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Geometry Question
  1. Geometry question (Replies: 4)

  2. Geometry Question (Replies: 1)

Loading...