## 2. Two-dimensional objects

We are familiar with a range of shapes that exist in a single plane and are defined by one or more lines (sides) that together enclose the object. Regular objects are those that belong to a small number of families with simple properties, such as all sides are a straight line. A circle and related shapes called ellipses are defined by a single line that has no ends (that is it is joined back onto itself). Shapes can be defined by two lines, whose ends join and at least one of which must be curved – a semicircle (half circle) is a shape made up from one straight line and one curved line.

Shapes defined by straight lines alone must have at least three sides. Triangles have three sides, quadrilaterals have four sides, and shapes with more than four sides are collectively known as polygons. Within these classes, there may be special cases. For instance, a square is a quadrilateral where all sides are the same length, opposite pairs of sides are parallel to each other and each angle where adjacent sides meet is a right angle (90°). An equilaterial triangle has all three sides the same length, and each angle where adjacent sides meet is 60°.