Geometry - Can a trapezoid ever be a kite, and vice versa?

[luke8ball]

Homework Statement

Can a trapezoid ever be a kite?
Can a kite be a trapezoid?

2. The attempt at a solution

I believe that the answer to both is no.

1. If a trapezoid was a kite, wouldn't the pair of parallel sides, along with the congruent consecutive sides, imply that it was a parallelogram? But a trapezoid only has one pair of parallel sides?

2. If a kite was a trapezoid, then wouldn't it have two pairs of opposite congruent angles, rather than exactly one?

I feel like my answers are correct, it's just that they don't seem mathematically sound. Any help is appreciated. :)

 

[ehild]

Read http://www.mathsisfun.com/quadrilaterals.html, and see the picture:

The definition of trapezoid does not say that the other sides can not be also parallel.

Is square a trapezoid?

The definition of kite does not say that the the other pair of opposite angles can not be also equal.

Is square a kite?

Are both quadrilaterals?

ehild