KnowraCeva's theoremLinked fromLinked fromThe 16 pages that link to Ceva's theorem, each with the reason it gives.All 16Related 10Compared with 6OrthocenterRelated: It provides a general concurrency framework for the triangle’s three altitudes.Triangle geometryRelated: It tests whether cevians meet at one point using ratios on the opposite sides.Angle bisector theoremRelated: Its product of side ratios can establish concurrence of triangle angle bisectors.Miquel's theoremCompared with: Both are classical concurrency theorems, but Miquel's concerns circles rather than cevians.Menelaus's theoremCompared with: It is the concurrency counterpart to Menelaus's collinearity criterion.Triangle centersRelated: It can establish concurrency for lines defining triangle centers.Intercept theoremCompared with: It uses triangle ratios for concurrence rather than proportional segments cut by parallels.Morley's trisector theoremRelated: It provides a useful framework for analyzing lines drawn from triangle vertices.Pappus's hexagon theoremCompared with: It is a classical incidence result about concurrency rather than Pappus's collinearity.Barrow's inequalityRelated: It illustrates the broader family of classical theorems organized around triangle points and lines.Bottema's theoremRelated: It provides a standard ratio criterion for concurrency, though Bottema’s construction uses perpendicularity.Droz-Farny line theoremCompared with: It also turns side-intersection data into a global triangle relation, but tests concurrency rather than midpoint collinearity.Incenter–excenter lemmaRelated: It can establish concurrence of angle-bisector lines in center proofs.Seven circles theoremRelated: Its ratio-based approach parallels Menelaus-style proofs of incidence conclusions.Thomsen's theoremCompared with: Unlike this metric-free closure, Ceva's criterion uses ratios along triangle sides.Van Lamoen circleRelated: The shared cevian point that partitions the triangle is governed by cevians’ concurrency.
KnowraCeva's theoremLinked fromLinked fromThe 16 pages that link to Ceva's theorem, each with the reason it gives.All 16Related 10Compared with 6OrthocenterRelated: It provides a general concurrency framework for the triangle’s three altitudes.Triangle geometryRelated: It tests whether cevians meet at one point using ratios on the opposite sides.Angle bisector theoremRelated: Its product of side ratios can establish concurrence of triangle angle bisectors.Miquel's theoremCompared with: Both are classical concurrency theorems, but Miquel's concerns circles rather than cevians.Menelaus's theoremCompared with: It is the concurrency counterpart to Menelaus's collinearity criterion.Triangle centersRelated: It can establish concurrency for lines defining triangle centers.Intercept theoremCompared with: It uses triangle ratios for concurrence rather than proportional segments cut by parallels.Morley's trisector theoremRelated: It provides a useful framework for analyzing lines drawn from triangle vertices.Pappus's hexagon theoremCompared with: It is a classical incidence result about concurrency rather than Pappus's collinearity.Barrow's inequalityRelated: It illustrates the broader family of classical theorems organized around triangle points and lines.Bottema's theoremRelated: It provides a standard ratio criterion for concurrency, though Bottema’s construction uses perpendicularity.Droz-Farny line theoremCompared with: It also turns side-intersection data into a global triangle relation, but tests concurrency rather than midpoint collinearity.Incenter–excenter lemmaRelated: It can establish concurrence of angle-bisector lines in center proofs.Seven circles theoremRelated: Its ratio-based approach parallels Menelaus-style proofs of incidence conclusions.Thomsen's theoremCompared with: Unlike this metric-free closure, Ceva's criterion uses ratios along triangle sides.Van Lamoen circleRelated: The shared cevian point that partitions the triangle is governed by cevians’ concurrency.