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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 xaxis, and the vertical axis is usually called the yaxis.
 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 xaxis and yaxis.
 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.
 OneDimensional – Having length but no width or height.
 Perspective – A technique of representing threedimensional objects and their relationships to each other on a twodimensional 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 threedimensional figure.
 Square – A quadrilateral with four right angles and four congruent sides.
 Squares have all of the properties of parallelograms, rectangles, and rhombi.
 ThreeDimensional – Having length, width, and height.
 Width – The measurement taken from one side of an object to the other side (or front to back).
 ZeroDimensional – 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 
 Zerodimensional: One point defines a point.
 Onedimensional: Two points define a line.
 Twodimensional: Three noncollinear points define a plane.
 Threedimensional: 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 
ThreeDimensional 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 threedimensional space.

 Ex 2. It is true that one can use twodimensional objects to build threedimensional objects.

 Ex 3. It is true that many rules concerning twodimensional geometry have threedimensional analogues.
 In other words, the rules of twodimensional geometry can be applied to threedimensional solids.

Important!
Practice (Apex Study 11.1)
 Try practice problems on Pgs 1, 10
 Mandatory: write and answer problems on Pg 11
 1 Quiz
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