KnowraSimilar trianglesLinked fromLinked fromThe 18 pages that link to Similar triangles, each with the reason it gives.All 18Broader topic 1Related 13Narrower topic 3Compared with 1Pythagorean theoremRelated: Altitude constructions split a right triangle into smaller similar triangles, yielding algebraic proofs.MagnificationNarrower topic: Optical magnification often follows from proportional sides in ray diagrams.Ptolemy's theoremRelated: A standard proof constructs similar triangles whose side ratios yield the diagonal identity.Thales of MiletusRelated: Reports credit Thales with using proportional triangles to estimate inaccessible heights.Similarity transformationBroader topic: Their proportional sides are the central triangle-level consequence of similarity.Angle bisector theoremRelated: An auxiliary parallel line creates similar triangles that yield the side ratio.Intersecting chords theoremRelated: The intersecting chords proof identifies a pair of similar triangles.Cross-staffRelated: The instrument’s angular scale relies on fixed geometric proportions.Tangent–secant theoremNarrower topic: The tangent–secant relation can be derived by identifying similar triangles formed by a tangent and secant.Intercept theoremRelated: A parallel cut creates a smaller triangle similar to the original, yielding the segment ratios.Intersecting secants theoremRelated: The triangles formed by the secants and chords establish the products’ equality.Pedoe's inequalityRelated: Similarity is precisely the equality case of Pedoe's inequality.Playfair's axiomRelated: The axiom permits Euclidean constructions of distinct similar triangles at different scales.Butterfly theoremRelated: Similar-triangle arguments turn circle-intersection relations into midpoint ratios.Geometric mean theoremRelated: The three triangles formed by the altitude are pairwise similar, yielding the squared-length relation.Jacob’s staffRelated: The instrument’s geometry relates staff positions to sighting angles through triangle proportions.Equal Incircles TheoremCompared with: Their inradii scale with size; equal radii require matching scale as well.Haruki's theoremNarrower topic: Angle-chasing often reduces circle geometry length claims to proportional sides.
KnowraSimilar trianglesLinked fromLinked fromThe 18 pages that link to Similar triangles, each with the reason it gives.All 18Broader topic 1Related 13Narrower topic 3Compared with 1Pythagorean theoremRelated: Altitude constructions split a right triangle into smaller similar triangles, yielding algebraic proofs.MagnificationNarrower topic: Optical magnification often follows from proportional sides in ray diagrams.Ptolemy's theoremRelated: A standard proof constructs similar triangles whose side ratios yield the diagonal identity.Thales of MiletusRelated: Reports credit Thales with using proportional triangles to estimate inaccessible heights.Similarity transformationBroader topic: Their proportional sides are the central triangle-level consequence of similarity.Angle bisector theoremRelated: An auxiliary parallel line creates similar triangles that yield the side ratio.Intersecting chords theoremRelated: The intersecting chords proof identifies a pair of similar triangles.Cross-staffRelated: The instrument’s angular scale relies on fixed geometric proportions.Tangent–secant theoremNarrower topic: The tangent–secant relation can be derived by identifying similar triangles formed by a tangent and secant.Intercept theoremRelated: A parallel cut creates a smaller triangle similar to the original, yielding the segment ratios.Intersecting secants theoremRelated: The triangles formed by the secants and chords establish the products’ equality.Pedoe's inequalityRelated: Similarity is precisely the equality case of Pedoe's inequality.Playfair's axiomRelated: The axiom permits Euclidean constructions of distinct similar triangles at different scales.Butterfly theoremRelated: Similar-triangle arguments turn circle-intersection relations into midpoint ratios.Geometric mean theoremRelated: The three triangles formed by the altitude are pairwise similar, yielding the squared-length relation.Jacob’s staffRelated: The instrument’s geometry relates staff positions to sighting angles through triangle proportions.Equal Incircles TheoremCompared with: Their inradii scale with size; equal radii require matching scale as well.Haruki's theoremNarrower topic: Angle-chasing often reduces circle geometry length claims to proportional sides.