# 11.1 – Three Dimensions

## Key Terms

• Axis – One of the two lines that form a Cartesian coordinate system.
• The horizontal axis is usually called the x-axis, and the vertical axis is usually called the y-axis.
• The plural of axis is axes.
• Cartesian Coordinate System – A coordinate system formed by two number lines, one horizontal and one vertical.
• They intersect at the zero point of each line.
• The number lines are called axes and are usually labeled the x-axis and y-axis.
• Height – The measurement taken from the bottom to the top of an object.
• Length – A measurement taken horizontally across the longest side of an object.
• Line Segment – A part of a line with endpoints at both ends.
• The symbol AB means “the line segment with endpoints A and B.” It is sometimes called a segment.
• One-Dimensional – Having length but no width or height.
• Perspective – A technique of representing three-dimensional objects and their relationships to each other on a two-dimensional surface.
• Point – The most basic object in geometry, used to mark and represent locations.
• Points have no length, width, or height.
• Solid – An object that has three dimensions: length, width, and height.
• Also called a solid figure or a three-dimensional figure.
• Square – A quadrilateral with four right angles and four congruent sides.
• Squares have all of the properties of parallelograms, rectangles, and rhombi.
• Three-Dimensional – Having length, width, and height.
• Width – The measurement taken from one side of an object to the other side (or front to back).
• Zero-Dimensional – Having no length, width, or height.

## Review

Dimensions What Can Be Measured Example Object
Zero Nothing Points
One Length Segments, Lines, Rays
Two Length, Width Polygons, Planes
Three Length, Width, Height Cubes, Solids

Dimensions
• Zero-dimensional: One point defines a point.
• One-dimensional: Two points define a line.
• Two-dimensional: Three non-collinear points define a plane.
• Three-dimensional: Four points define space.

## Notes

Item Two Dimensions Three Dimensions
Number of Axes 2 3
Point Notation (x, y) (x, y, z)
Real Examples Maps, Paintings Globes, Sculptures

Three-Dimensional Objects
• Built from 0, 1, and 2 dimensional objects
• Have length, width, and height
• Can be graphed using x, y, and z axes

Examples
• Ex 1. It is true that, in geometry, a solid may exist in three-dimensional space.
• Ex 2. It is true that one can use two-dimensional objects to build three-dimensional objects.
• Ex 3. It is true that many rules concerning two-dimensional geometry have three-dimensional analogues.
• In other words, the rules of two-dimensional geometry can be applied to three-dimensional solids.