Geometry Question

  • #1
physics kiddy
135
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.
 

Attachments

  • Question.jpg
    Question.jpg
    4.5 KB · Views: 346

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,915
Write out the sum of angles of the yellow pentagon.

ehild
 

Attachments

  • quadrilateral.JPG
    quadrilateral.JPG
    9.5 KB · Views: 396
  • #3
physics kiddy
135
1
It's 540 degrees.
 
  • #4
ehild
Homework Helper
15,543
1,915
It's 540 degrees.

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:
  • #5
NascentOxygen
Staff Emeritus
Science Advisor
9,242
1,073
In triangle QOP, determine angle QOP, hence determine reflex angle QOP.
 
  • #6
ehild
Homework Helper
15,543
1,915
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
 
  • #7
physics kiddy
135
1
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.
 
  • #8
ehild
Homework Helper
15,543
1,915
I would like to see that solution from the book so much! Could you please show it?:smile:

ehild
 

Suggested for: Geometry Question

Replies
16
Views
236
Replies
52
Views
1K
Replies
1
Views
309
Replies
21
Views
1K
Replies
17
Views
800
Replies
7
Views
1K
  • Last Post
Replies
8
Views
1K
Replies
2
Views
644
Replies
13
Views
3K
Top