How to Explain Why a Square Is Always Symmetric

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Symmetry refers to the division of a shape. If a shape is divided in half and the halves are exactly the same, the shape is symmetrical. Squares are always symmetric, because no matter whether you flip, slide or rotate them, their halves will always be identical. Additionally, the halves of the squares will remain identical no matter which way you divide them -- whether you do so vertically, horizontally or diagonally.

Congruent Angles

Two objects are congruent if they are the same shape and size. A square is a two-dimensional shape that features four sides of equal lengths and four 90-degree angles. This means all the sides of a square are congruent with one another, and all the angles of a square are congruent with one another. Congruent objects can be flipped, slid or rotated and still stay symmetrical. Because the four lines and angles of squares are always the same, the two sides of the square will also match up no matter how you divide the square. In contrast, while a pentagon might be symmetric if it's cut in half vertically, it won't be symmetric if it's cut in half horizontally, because the top of the pentagon comes to a pointed angle, whereas the bottom of it does not.