Points - Lines - Planes

Geometry is a mathematical system built on accepted facts, basic terms, and definitions. In geometry, some words such as point, line, and plane are undefined. Undefined terms are the basic ideas that you can use to build the definitions of all other figures in geometry. Although you cannot define undefined terms, we can still express ways that we relate and represent these undefined terms.

Point

A point identifies a location. It has no dimensions, but is represented by a dot. A common way of assigning a point location is by using a coordinate system.

Points are named using a capital letter, such as point P.

Line

A line is a straight path, Lines have one dimension, length, but no width. Lines extend forever in opposite directions.

Lines are named either by a lowercase script letter, or by two points on the line.

Plane

A plane is a flat surface the has two dimensions, length and width, but no height. Planes extend in all directions infinitely.

Planes are named using a script capital letter or three non-collinear points in the plane. Plane ABC or Plane R.

Geometry Basics - Problem 1

Now the undefined terms of geometry can be used to define other figures such as endpoints, line segments, and rays. All other figures are constructed using the undefined terms of geometry, simply put, every geometric figure is a set of points.

Segment

A line segment is a part of a line consisting of two different points on the line called endpoints and all the points in between.

Line segments are named by the endpoints and are denoted by an overbar.

Ray

A ray is a part of a line that starts at an endpoint and extends in one direction.

Rays are named by their endpoint followed by any other point on the ray, with an arrow overhead, such that the end of the name shows the direction of the ray.

Opposite Rays

Opposite rays are two rays sharing a common endpoint extending in opposite directions, such that they form a line.

Opposite rays are named using the common endpoint and any other point on each respective ray.

Geometry Basics - Problem 2

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