It all depends on your definition of "side" and "figure". Do you mean two-dimensional figures specifically? Do you mean "side" as a straight segment connecting to another straight segment forming an angle between them? The question is just loaded even if you do say "yes" to the above questions because mathematicians are still arguing about whether or not a circle (for instance) has no sides, an infinite number of sides, or one curved side. (If you go over to the DrMath website, you can see a long discussion about it.) If the answer to the first question is "no", then a single point has no sides (since it has a dimension of 0).
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A Quadrilateral. Figures that have four equal sides are called squares. Whereas, other figures that have four unequal sides are called quadileterals
The Definition of Congruent Figures (which is a proof) says that if two figures have corresponding sides congruent and corresponding angles congruent, then the figures are to be congruent.
a square and a rhombus
If the two figures are the same shape. Also if the ratios of the lengths of the corresponding sides are equal.
The ratio between corresponding sides or angles of similar triangles are equal