Understanding basic geometry is essential to many designers, for example when surveying a space and when drawing the space. Although CAD software used for this purpose greatly simplify the drawing process, they still rely on the same geometry principles and terminology.
| Angles | 2-dimensional geometry | 3-dimensional geometry |
Angles
Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.
There are many different type of angles:
Acute
Angle |
Right Angle
|
Obtuse Angle
|
Greater than 0 degree
and less than 90 |
Exactly 90 degrees |
Greater than 90 degrees and less
than 180 |
|
|
|
Straight Angle |
Reflex Angle |
Revolution Angle |
Exactly 180 degrees |
Greater than 180 degrees and less
than 360 |
Exactly 360 degrees |
|
|
|
Two angles that have the same measure are called Congruent
angles. For example if X is 15 degrees and Y also 15 degrees,
then X is congruent to Y.
Two angles are called Supplementary when
their measure adds up to 180. For example, if X is 60 degrees
and Y 120 degrees, 60 + 120 = 180. X and Y are supplementary.
Two angle are called Complementary if their
measure adds up to 90. For example, if X is 60 degrees and
Y is 30 degrees, 60 + 30 = 90. X and Y are complementary.
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2-dimensional
geometry
Working drawings are 2-dimensional. A floor plan, for example,
is a two dimensional representation of a room or house. So
is an elevation.
Below are some examples of calculations in 2-dimensional geometry:
r = radius, h = height
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3-dimensional geometry
A 3-dimensional representation is needed to clearly understand what a space or object will look like when it is finished. 3D drawings of man made environments often use a combination of simple solids such as cubes, spheres, cylinders, pyramids or cones to create more complex shapes. Drawing with CAD follows the same principles and it is better to combine solids rather than attempt to create a complex object from scratch.
Below are some examples of calculations in 3-dimensional geometry: r = radius, h = height
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