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Why are squares rectangles but not all rectangles are squares?

Karen Wright

in Homework Help

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Karen Wright on September 19, 2018

A rectangle has four sides and four right-angled corners. A square has four sides and four right-angled corners and has all sides of equal length. A rectangle is defined as to have: . Four sides; . All angles equal 90°; . Two pairs of opposite sides of equal length. A square is defined as: . Four sides; . All angles equal 90°; . All four sides of equal length. The first two properties are common to the square andrectangle. The third property is different: For a square all the sides are of equal length. Can be dividedinto two pairs of opposite sides of equal length, which is the third property of the rectangle. Therefore all squares are rectangles. For a rectangle, with two pairs of opposite sides of equal lengthmeans that the two pairs can have different lengths (as long as thesides in each pair are of the same length). The two sets have the same length, in which case the rectangle is a square, but if the two sets have different lengths, then all four sides, not all havethe same length, and therefore are not square. Therefore not all rectanglesare squares. The squares form a subset of the rectangles (squares âŠ'rectangles) where the two sets of pairs of opposite sides haveequal length (i.e., all four sides are of equal length).


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