The four properties that govern all of geometry are point, line, plane and solid. Geometry is divided into two distinct categories. Plane geometry studies two-dimensional shapes, or items on a flat surface, while solid geometry studies three-dimensional objects.
A point is a positional starting point with no dimensions. A line is the shortest distance between two points and is one-dimensional. A plane is two-dimensional and can be drawn on a flat surface. Examples include a square, triangle and rectangle. Solids, like spheres, are three-dimensional.
Two-dimensional shapes include polygons and curved objects. Regular polygons have straight sides which are the same length and angles with the same measurement. One example is the equilateral triangle, where each angle measures 60 degrees. Variations include the isosceles triangle, which has two angles the same, and the scalene triangle, where all angle measurements are different. All the angles of any triangle must add up to 180 degrees.
The most common curved shape is the circle. Circles are measured by the radius, the distance from the point to the outside of the circle, the diameter, which is the midpoint across the circle, and the circumference. The radius is always the same measurement, no matter where the measurement is taken.
In solid geometry, which adds the third dimension, a circle becomes a sphere. Like the circle, a sphere is perfectly symmetrical and has no edges or corners. The measurements from the center point to any place on the surface are equal.