0
$\begingroup$

A quadrilateral with one diagonal that bisects opposite angles and another diagonal that does not bisect opposite angles may or may not be a kite.

We know that a kite is a quadrilateral if it has two pair of equal and adjacent sides, of which the diagonals intersects at right angles, but how could we conclusively prove the validity of this statement?

  • 2
    This may depend on whether a (non-convex) symmetric dart counts as a kite. The words "is" in the question and "would" in the statement look a bit odd.2012-02-02
  • 0
    The statement is logically of the form "$A$ or not $A$" so it is a tautology, and trivially valid. What do you really mean to ask?2012-02-02
  • 0
    @GerryMyerson - This proposition is not a tautology. It says that a quadrilateral with this property may be a kite, and that a quadrilateral with this property may be not a kite. If all quadrilaterals with this property are kites, or if all quadrilaterals with this property are non-kites, then this proposition is false. To prove the validity of this proposition, one would have to exhibit a kite with this property, and also a non-kite with this property.2012-02-04
  • 1
    @DavidWallace, we have different ideas about mathematical English. I interpret "a square may or may not have five sides" as "(a square may have five sides) or (a square may not have five sides)" and thus true, even though there isn't a square with five sides.2012-02-04
  • 0
    @GerryMyerson - then maybe the OP needs to clarify which interpretation he/she has in mind.2012-02-04

1 Answers 1