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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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  • $\begingroup$ What definitions of kite and trapezoid are you using? $\endgroup$ – Joel Reyes Noche Feb 23 '15 at 4:11
  • $\begingroup$ A kite has two pairs of consecutive sides equal, diagonals are perpendicular and one diagonal is bisected, one diagonal bisects a pair of opposite angles and one pair of opposite angles are congruent . Trapezoid has two parallel sides. $\endgroup$ – Lulu Uy Feb 23 '15 at 4:19
  • $\begingroup$ Trapezoid has one pair of parallel sides.* $\endgroup$ – Lulu Uy Feb 23 '15 at 4:20
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    $\begingroup$ I assume that you define kites and trapezoids as quadrilaterals. But you'll need to be more specific. You say "one" three times in your first comment, and another time in your second comment. But when you say "one," do you mean "exactly one" or "at least one"? $\endgroup$ – Joel Reyes Noche Feb 23 '15 at 4:24
  • $\begingroup$ Sorry, I mean exactly one. $\endgroup$ – Lulu Uy Feb 23 '15 at 4:44
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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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  • $\begingroup$ I see...the reason I ask without giving a definition is that I take many math tests and have seen problems that ask this same question without giving a definition. $\endgroup$ – Lulu Uy Feb 23 '15 at 4:45
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    $\begingroup$ It is a big problem when those who construct tests do not explicitly state the definitions of the terms they use. $\endgroup$ – Joel Reyes Noche Feb 23 '15 at 4:50

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