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Can a square be a kite or a trapezoid and can a trapezoid or kite be a square? I don't think so, but this question is debated everywhere. The only reason a square is considered a rectangle and rhombus is because it is essentially a combination of the two. A trapezoid and kite had nothing to do with the creation of the square, therefore I don't think a square can be a kite/trapezoid and vice versa.

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1 Answer

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Your answer greatly depends on what definitions you are using.

For example, according to Wikipedia,

Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition) [...]. Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definition) [...].

So, for example, if you use the exclusive definition of a trapezoid, then a square is not a trapezoid. But if you use the inclusive definition of a trapezoid, then a square is a trapezoid.

The situation is the same for kites. You'll need to specify your definition before you can answer your question.

Edit: You state in a comment that you're using the exclusive definition of a trapezoid. So,

A square is not a trapezoid.

Now, I assume that by kite you mean "a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other," then

A square is a kite.

Using the definition of a square,

A trapezoid is not a square.

A kite is not necessarily a square.

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