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Your real life may or may not ever involve congruent triangles. The reason why they are studied is because in mathematics, everything interconnects. Geometry is a tool that is used to help understand many other types of mathematical problems; combined with algebra you get analytical geometry, which is necessary to be able to do calculus, and calculus is essential for virtually any scientific or technical activity. But some people never use it. There are large numbers of people who never have any need for any form of mathematics more advanced than simple arithmetic.

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