All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Quadrilateral Concurrency (Posted on 2008-03-06) Difficulty: 3 of 5
Prove that the four lines obtained by joining each vertex of a quadrilateral to the centroid of the triangle determined by the other three vertices are concurrent.

See The Solution Submitted by Bractals    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): Can you provide insight? | Comment 4 of 6 |
(In reply to re(2): Can you provide insight? by Dej Mar)

After checking it out with Geometer's Sketchpad.
For parallelograms,
it looks like AA' and CC' define the same line as
do BB' and DD'. For all other quadrilaterals (
convex, concave, even reflex) the four lines
are concurrent. Note that for some quadrilaterals,
X = X' and we only have three lines. But, the three
lines are concurrent.
So maybe instead of saying that the four lines
are concurrent, we should say the "four" lines
pass through the same point.

Edited on March 9, 2008, 4:53 am
  Posted by Bractals on 2008-03-09 04:50:35

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information