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A speed square or rafter angle square is a tool that can be used as a saw guide. The purpose of this tool is to guide the saw when making short 45 and 90 degree angles.
The purpose of trigonometry is to gather as much accurate measurements of distances given little information about angles or other distances. It is used in engineering, astronomy, city planning, drafting and designing, and construction.
Some shapes have angles and so they are important in defining the shapes. And angles are absolutely critical for angles. They are the very essence of their existence: if it were not for angles then there would be no angles.
Yes, congruent angles are angles that have the same measure.
They are used to support other elements of the structure as well as to divert the load to support columns which are usually based in the bed rock.