A quadrilateral is a ______ if and only if its diagonals are perpendicular.

I think the answer is either KITE or else RHOMBUS, but I'm not sure which one.
Help!
Thanks!

"Kite" is the best answer.

You're correct that both kites and rhombi have perpendicular diagonals (as do squares).

But, just as a square is a type of rhombus (with 90-degree angles), a rhombus is a type of kite (with sides that are all equal). So "kite" is the more general classification, and that is the correct solution.

Rita the dog's answer demonstrates that there are irregular quadrilaterals with perpendicular diagonals. However, the "if and only if" proposition requires that we restrict the answer to a particular type, and I couldn't think of one more general than a kite. If there is one, then it's better.

Report Abuse

The diagonals of a kite are perpendicular.
The diagonals of a rhombus are perpendicular.

Neither converse is true.

Consider the quadrilateral whose vertices are (-1, 0), (0,-3), (2, 0) and (0, 2). It is neither a kite nor a rhombus, but its diagonals are pieces of the x and y axes intersecting at the origin, so its diagonals are perpendicular.

It can also be a kite since it isn't specified that the diagonals must bisect each other

It's a rhombus.