A synthetic proof in geometry is a proof that reasons directly about geometric objects and their relations using geometric axioms and theorems. It contrasts with an analytic proof, also called a coordinate proof, which uses coordinate calculations in analytic geometry (Beutelspacher and Rosenbaum 1998, p. viii; Baldwin and Mueller 2024, p. 4).
Synthetic Proof
See also
Analytic Geometry, Analytic Proof, ProofExplore with Wolfram|Alpha
References
Baldwin, J. T. and Mueller, A. "Supplement: Focusing a GeT Course on Axiomatic Systems for Geometry." Jan. 2, 2024. https://www.math.uic.edu/~jbaldwin/pub/supp2Dec3.pdf.Beutelspacher, A. and Rosenbaum, U. Projective Geometry: From Foundations to Applications. Cambridge, England: Cambridge University Press, 1998.Cite this as:
Weisstein, Eric W. "Synthetic Proof." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SyntheticProof.html