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11.1 – Three Dimensions
- 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.
||What Can Be Measured
||Segments, Lines, Rays
||Length, Width, Height
- 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.
|Number of Axes
||(x, y, z)
- Built from 0, 1, and 2 dimensional objects
- Have length, width, and height
- Can be graphed using x, y, and z axes
- 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.
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