geometric proofs
Logical figure arguments
Geometric proofs are step-by-step logical arguments that establish the truth of geometric statements.
Each step follows from definitions, axioms, or previously proven theorems.
The classic form presents a series of statements with justifications, building toward a conclusion: We had to write two-column proofs in geometry class.
Proofs may demonstrate that angles are congruent, lines are parallel, or shapes have certain properties.
- QEDProof-concluding abbreviation
- angleGeometric measure of rotation
- right angleExactly ninety degrees
- theoremDemonstrated logical conclusion
- postulateAssumed starting point
polygon · congruence · corollary · axiom · similarity · Euclid · constructions · Descartes · symmetry · plane · point · deductive reasoning · Pythagoras · definition · trigonometry · lemma · bisector · parallel lines
- ancient mathalgebra, arithmetic, fractions, addition, subtraction
- liberal artshumanities, trivium, philosophy, history, classical education
- Pythagorastheorem, triangles, math, numbers, ratios
- geometry problemssquaring the circle, quadrature
- geometryangles, circles, angle, shapes, lines
- ancient textsscrolls, scroll, Euclid's Elements, Epic of Gilgamesh, codex
geometric proofstrial and error
Learning through repeated attempts
empirical verification · estimation · computer simulation · simulation · arithmetic operations
geometric proofseducated guesses
Estimates grounded in knowledge
empirical observation · conjecture · inductive reasoning · hand-waving · pattern recognition