it's a subject because it explains about all types of shapes that you can know and it also teaches you how to calculate the area and perimeter of the shape that you are finding.
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The subject of trigonometry is in geometry.
Yes
The Greeks, they were highly interested in shapes and that kind of thing.
Analytical geometry was founded by the French mathematician, Renee Descartes. As for subsequent contributors to that subject, I will leave that for other contributors to add.
Reflection of an object is the flip of that subject on a particular line, that is called line of reflection.