A Shape is what is formed when three or more lines intersect and form a geometric object with area and a perimeter. Put simply, a shape is a geometric object that has an area.
Area describes the space that is “closed off” by the lines. Think of it as all the points that a particular shape contains.
Perimeter describes the lengths of all lines that compose the shape.
Shapes are composed of edges which meet at vertices.
An edge is the line that forms one side of a shape.
A vertex describes the point at which two lines (edges) join. As a consequence of this, an angle is formed by the two edges at this vertex.
An Irregular Shape is one where its sides and interior angles are not all the same.
An Regular Shape is one where its sides and interior angles are all the same.
A Cyclic Shape is one whose vertices all lie on a single circle. In other words, this shape is inscribed.
A convex shape is one such that all of its interior angles are less than $180^\circ$.
A concave shape is one such that at least one of its interior angles are greater than $180^\circ$.
An equilateral shape is a shape such that all sides are the same length. For instance, a square is equilateral.
A regular convex shape is a regular shape that is also convex.
A simple shape is one that does not intersect itself.
A equiangular shape is one such that all corner angles are equal.
A tangential shape is one such that all sides are tangent to a circle. In other words, the circle is inscribed inside this shape.
Congruence describes a property of two shapes such that they have the same shape and size.
Similarity describes the relationship between two shapes such that they have the same “shape”. In other words, the shapes are just about the same, but they have been moved, rotated, reflected, or scaled:
Under construction!