Geometry was very important to the ancient Romans for the purposes of civil engineering and navigation just to name only two of the reasons of which there were many more reasons.
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Lone electron pairs give the geometry a triangular base.
Most geometry is used in real life situations. Logic can determine which outcomes are and are not possible. In geometry negative answers are posible, but if the problem is dealing with a real life situation, their shouldn't be used. This can determine that a mistake has been made in the calculation of the answer or their is an unfound positive answer along with the negative answer.
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because we use it to calculate/measure things in science for example we use maths to calculate the distance of stars from the earth