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

Home > Shapes > Geometry
Trapezoid Proof (Posted on 2008-04-17) Difficulty: 3 of 5
Two opposite sides of a quadrilateral are the same length. The diagonals of the quadrilateral are also the same length. Prove the quadrilateral is a trapezoid.

No Solution Yet Submitted by Brian Smith    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 4

Let ABCD be the quadrilateral with
|AB| = |CD| and |AC| = |BD|.
Triangles ABC and DCB are congruent by SSS
  ==> angle ABC = angle DCB = angle BCD
Triangles BAD and CDA are congruent by SSS
  ==> angle CDA = angle BAD = angle DAB
360 = angle ABC + angle BCD +
      angle CDA + angle DAB
    = 2(angle ABC) + 2(angle DAB)
    or
180 = angle ABC + angle DAB
  ==> DA || BC
  ==> ABCD is a trapezoid.
 

  Posted by Bractals on 2008-04-17 13:01:22
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 (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information