By definition, an equilateral shape is a shape that has all its sides an equal length. Take, for example, the Equilateral triangle.
This is an equilateral triangle. An equilateral triangle is a 3 sided, 2-dimensional shape like any other triangle however as the name suggests all sides and angles of this triangle are equal. All angles are 60 degrees and add up to 180 degrees.
A Quadrilateral shape by definition is a four-sided, 2D shape. Unlike the Equilateral shapes, quadrilateral shapes do not have to be equal length. Some examples of quadrilateral shapes are the following shapes below.
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All these shapes are quadrilateral shapes. Some examples of a quadrilateral shape is a square and a parallelogram.
A square has 4 equal sides and equal angles. It is both a equilateral and quadrilateral shape, making it the only shape that is both an equilateral and quadrilateral. The diagonals of the square are equal as well.
The parallelogram unlike the square does not have 4 equal sides and angles, instead it is a 4 sided regtangular shape with opposite sides parallel to eachother. The opposite angles are also congruent (equal in length) and it's diagonals bisect eachother.
