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The 18 pages that link to Similar triangles, each with the reason it gives.

• Pythagorean theoremRelated: Altitude constructions split a right triangle into smaller similar triangles, yielding algebraic proofs.

• 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.

• 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.

• 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.