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

Home > Shapes
Quadrilateral fill in the blank (Posted on 2018-01-25) Difficulty: 3 of 5
A quadrilateral is a _________ if and only if the sum of the squares of its sides is equal to the sum of the squares of its diagonals. Prove it.

No Solution Yet Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
A draft for solution Comment 2 of 2 |
If a quadrilateral verifies that property then the middle points of both diagonals are a single point (applaying Euler's theorem for quadrilaterals), and this implies that it is a paralelogram. 

Euler:
D^2+d^2 = a^2+b^2+c^2+d^2+4MN 
where MN is the segment uniting the middle points of both diagonals. 
••••
Also for the theorem of cosine it is very easy to show that each paralalogram verifies that property. 

  Posted by armando on 2018-01-27 09:50:42
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
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

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