It can be used as a side length, which has many possibilities to figure with.
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The altitude of a triangle IS a geometric concept so it intersects geometry in its very existence.
Geometry is used mainly in construction.
In geometry, a perpendicular segment that connects a vertex to its opposite side is the altitude of a triangle. Triangles have three altitudes, according to this definition for altitude.
The answer is in the word -- Geo means 'Earth', and 'metry' means 'measure'. Geometry means to measure the earth. Ancient Egyptians used a form of simple geometry. When buildings or crops needed to be plotted out, geometry was used.
Geometry is very important because you practically see it everyday. Everything is geometry. Humans are geometry. planets are geometry. If you don't really understand how much geometry is used and important, then you should try to see somebody for geometry answers.