{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.trapezoid","code":"thing-q46303","url":"https://ver.cy/models/thing/q46303/","name":"trapezoid","alternateNames":["proper trapezoid","isosceles trapezoid","right trapezoid with exactly one pair of parallel sides","isosceles trapezoid with exactly one pair of parallel sides","bicentric trapezoid","midsquare trapezoid","tangential trapezoid","right trapezoid","irregular trapezium","right tangential trapezoid"],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A quadrilateral with at least one pair of parallel sides, called a trapezium in British usage, with special cases such as the isosceles trapezoid with equal legs, the right trapezoid with a right angle, and under the inclusive definition parallelograms as well, and with properties such as the midsegment and area formula based on the parallel sides and height; trapezoids appear in geometry education, architecture and engineering.","purpose":"Let an agent explain trapezoids and their definitions and properties, compute area and other measures, distinguish inclusive and exclusive definitions and British usage, and support geometry learning.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Parallel bases","Legs and height","Midsegment property","Terminology variation"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What a trapezoid is.","layers":[{"id":"definition","name":"Definition","description":"Definitions.","findings":[{"id":"definition-finding","name":"Definition","description":"Definitions.","questions":[{"text":"What is a trapezoid, how do inclusive and exclusive definitions differ, and how does British trapezium usage differ?","kind":"definition"},{"text":"Which definition applies in this curriculum?","kind":"boundary"}]}]},{"id":"special","name":"Special","description":"Special cases.","findings":[{"id":"special-finding","name":"Special","description":"Special cases.","questions":[{"text":"What are isosceles, right, bicentric and midsquare trapezoids, and what properties do they have?","kind":"definition"},{"text":"Which entry fits a specific case?","kind":"action"}]}]}]},{"id":"compute","name":"Compute","description":"Calculations.","layers":[{"id":"area","name":"Area","description":"Area and perimeter.","findings":[{"id":"area-finding","name":"Area","description":"Area.","questions":[{"text":"How are the area, perimeter, midsegment and diagonals of a trapezoid computed?","kind":"action"},{"text":"How is the height found when not given?","kind":"action"}]}]},{"id":"prove","name":"Prove","description":"Proofs.","findings":[{"id":"prove-finding","name":"Prove","description":"Proofs.","questions":[{"text":"How are trapezoid properties proved, such as the midsegment theorem?","kind":"action"},{"text":"Which entry fits Euclidean geometry?","kind":"action"}]}]}]},{"id":"apply","name":"Apply","description":"Applications.","layers":[{"id":"applications","name":"Applications","description":"Trapezoids in practice.","findings":[{"id":"applications-finding","name":"Applications","description":"Applications.","questions":[{"text":"Where do trapezoids appear in architecture, engineering and numerical integration such as the trapezoidal rule?","kind":"provenance"},{"text":"Which entry fits the trapezoidal rule?","kind":"action"}]}]},{"id":"generalise","name":"Generalise","description":"Generalisations.","findings":[{"id":"generalise-finding","name":"Generalise","description":"Generalisations.","questions":[{"text":"How do trapezoids generalise in higher dimensions and non-Euclidean geometry?","kind":"definition"},{"text":"Which references are standard?","kind":"provenance"}]}]}]},{"id":"learn","name":"Learn","description":"Teaching and history.","layers":[{"id":"teach","name":"Teach","description":"Teaching trapezoids.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can trapezoids be taught with constructions and classification exercises?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]},{"id":"history","name":"History","description":"History of the terms.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the terms trapezoid and trapezium develop and diverge?","kind":"provenance"},{"text":"Which entry fits history of geometry?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Compute areas, angles and sides of trapezoids, stating which definition is used.","Explain the trapezoid and trapezium naming difference between dialects."],"mustNot":["Mix the inclusive and exclusive definitions within one problem or answer.","Mark a learner's work wrong because of a dialect naming difference.","Present an area formula without checking which sides are parallel."],"requiresHuman":["Grading a learner's work where the definition used is disputed."]},"ethics":{"considerations":["Learners can be confused or penalised by inconsistent definitions."],"affectedParties":["Learners","Teachers","Engineers and drafters"]},"owners":{"steward":"Nobody owns the concept; it is held in common by mathematics.","roles":[],"masterSystems":[]},"relations":[{"target":"Q39447036","type":"parent","note":"registry parent class"},{"target":"convex quadrilateral","type":"related","note":"category"},{"target":"triangle","type":"related","note":"related polygons"},{"target":"curvature","type":"related","note":"another geometric entry"},{"target":"difference","type":"related","note":"contrasting definitions"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.trapezoid","Wikidata: Q46303 (https://www.wikidata.org/wiki/Q46303)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["One pair of parallel sides","Special cases isosceles and right","A parallelogram has two pairs; British trapezium and trapezoid are swapped","A four-sided figure with two parallel sides."]},"capabilities":{"applicability":"required","items":["explain definitions and properties","compute area and measures","clarify terminology","support learning"]},"hazards":{"applicability":"required","items":["Confusing trapezoid and trapezium across dialects","Applying the exclusive definition inconsistently","Area formula errors"]},"interfaces":{"applicability":"required","items":["Mathematical definitions in curricula","Terminology conventions by country"]},"context":{"applicability":"required","items":["Quadrilaterals with parallel sides.","general trapezoids","isosceles trapezoids","right trapezoids","bicentric and other special trapezoids","parallelograms under the inclusive definition"]}},"sources":[{"title":"Wikidata item Q46303: trapezoid","url":"https://www.wikidata.org/wiki/Q46303","note":"identity and sense of the item"},{"title":"Wikipedia: Trapezoid","url":"https://en.wikipedia.org/wiki/Trapezoid","note":"general description of the item"}],"openQuestions":["Should isosceles trapezoid be a separate entry?","How should curriculum standards be linked?","How should terminology be documented?"],"resources":{"spec":"/models/things/publications/thing-q46303/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q46303/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T00:11:07Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-06T19:52:00+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}