Horse riding and geometry are most commonly related using Pythagorean Theorem. Which can help calculate the best take off point for show jumping
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Geometry is used mainly in construction.
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.
In geometry, deductive rules can be used to prove conjectures.
Geometry is used by many things, in many different ways.