Difference between revisions of "1977 USAMO Problems/Problem 4"
(Created page with "== Problem == Prove that if the opposite sides of a skew (non-planar) quadrilateral are congruent, then the line joining the midpoints of the two diagonals is perpendicular to th...") |
|||
| Line 7: | Line 7: | ||
== See Also == | == See Also == | ||
{{USAMO box|year=1977|num-b=3|num-a=5}} | {{USAMO box|year=1977|num-b=3|num-a=5}} | ||
| + | {{MAA Notice}} | ||
[[Category:Olympiad Geometry Problems]] | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 18:05, 3 July 2013
Problem
Prove that if the opposite sides of a skew (non-planar) quadrilateral are congruent, then the line joining the midpoints of the two diagonals is perpendicular to these diagonals, and conversely, if the line joining the midpoints of the two diagonals of a skew quadrilateral is perpendicular to these diagonals, then the opposite sides of the quadrilateral are congruent.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 1977 USAMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
