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

 Trapezoid Proof (Posted on 2008-04-17)
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 | 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 (4)
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