a really great example of deduction

A famous example of deduction within Geometry is the Pythagorean Theorem.
A famous example of deduction within Analysis is the Binomial Theorem.
However, a deduction within Geometry suffers from the defect of being dependent upon a diagram that may be inaccurately drawn, and a deduction within Analysis suffers from the defect of requiring non-trivial knowledge of the real-number system. Is there any deduction of interest that has neither defect? Yes: The 6-People Theorem.
keywords: motivational examples, engagement with mathematics