question archive All squares are rectangles

All squares are rectangles

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All squares are rectangles. Not all rectangles are squares.

A quadrilateral is a rectangle if all four internal angles are ##90^@##.

A quadrilateral is a square if all four internal angles are ##90^@## and all four sides are equal in measure.

Note that the first condition for a square is the same as the only condition for a rectangle, and thus all squares are rectangles. However, there is no condition which requires a rectangle to have four equal sides, and thus not all rectangles are squares. For example:

The above is a rectangle, as all four angles are ##90^@##, but is not a square, as the two vertical sides are shorter than the two horizontal sides.


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