# 1.6 – Planes and the Space of Geometry

## Objectives

• Define the three dimensions of length, width, and height.
• Define and identify collinear points and coplanar points and lines.
• Identify objects that are zero-, one-, two-, and three-dimensional.
• Relate the concept of infinity to one-, two-, and three-dimensional objects.

## Key Terms

• Infinite – having no boundary or limit.
• Collinear – lying in a straight line. Three or more points are collinear if a straight line can be drawn through all of them.
• Plane – a flat surface that extends forever in all directions (infinite). A plane has no thickness, so it has only two dimensions (length and width).
• Coplanar – lying in the same plane. Four or more points are coplanar if there is a plane that contains all of them.
• Zero-Dimensional – having no length, width, or height (ex. points)
• One-Dimensional – having length but no width or height (ex. lines, line segments, rays)
• one-dimensional with infinite length: lines and rays
• one-dimensional with measurable length: line segments
• Two-Dimensional – having length and width but no height (ex. planes / flat surfaces you can’t pick up)
• Three-Dimensional – having length, width, and height (ex. solids, geometric space, our world, things you can grab and hold)

## Notes

Dimensions

Collinear
• If you have exactly two points, they will ALWAYS be collinear.
• If you have more than two points, they might be collinear, but they might not.
• Three or more points are collinear if a line can be drawn through ALL of them

Coplanar
• If three points are collinear, they are also coplanar
• Two lines are guaranteed to be coplanar if they lie in the same plane.
• Two lines and a point are guaranteed to be coplanar if they lie in the same plane.
• Four points are always coplanar if they lie on the same line (collinear) AND lie in the same plane.