{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.parallelogram","code":"thing-q45867","url":"https://ver.cy/models/thing/q45867/","name":"parallelogram","alternateNames":["Varignon parallelogram","rhomboid","Wittenbauer's parallelogram"],"kind":"thing","status":"published","version":"0.2.0-wave.3","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 two pairs of parallel sides, whose opposite sides are equal, opposite angles are equal and diagonals bisect each other; rectangles, rhombi and squares are special cases, its area is base times height, and the Varignon parallelogram formed by the midpoints of any quadrilateral sides is a classic result.","purpose":"Let an agent define the parallelogram and its properties, compute area, perimeter and angles, distinguish it from trapezoids and other quadrilaterals, and relay classic theorems and teaching approaches.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Two pairs of parallel sides","Diagonals bisect each other","Special cases: rectangle, rhombus, square","Vector parallelogram law"],"structure":{"bundles":[{"id":"define","name":"Define","description":"What a parallelogram is.","layers":[{"id":"definition","name":"Definition","description":"Definition and properties.","findings":[{"id":"definition-finding","name":"Definition","description":"Definition.","questions":[{"text":"What defines a parallelogram, and what properties follow?","kind":"definition"},{"text":"Is the shape a parallelogram, a trapezoid or another quadrilateral?","kind":"boundary"}]}]},{"id":"special","name":"Special","description":"Special cases.","findings":[{"id":"special-finding","name":"Special","description":"Special.","questions":[{"text":"How do rectangles, rhombi and squares relate to parallelograms?","kind":"definition"},{"text":"Which entry fits the special case?","kind":"action"}]}]}]},{"id":"compute","name":"Compute","description":"Calculation.","layers":[{"id":"area","name":"Area","description":"Area and perimeter.","findings":[{"id":"area-finding","name":"Area","description":"Area.","questions":[{"text":"How are area, perimeter and angles computed from sides, heights and angles?","kind":"action"},{"text":"What is the result for the values in question?","kind":"measurement"}]}]},{"id":"coordinates","name":"Coordinates","description":"Coordinate and vector methods.","findings":[{"id":"coordinates-finding","name":"Coordinates","description":"Coordinates.","questions":[{"text":"How is a parallelogram handled with coordinates and vectors, including the cross product for area?","kind":"action"},{"text":"Which entry fits vectors?","kind":"action"}]}]}]},{"id":"theorems","name":"Theorems","description":"Classic results.","layers":[{"id":"varignon","name":"Varignon","description":"Varignon parallelogram.","findings":[{"id":"varignon-finding","name":"Varignon","description":"Varignon.","questions":[{"text":"What does Varignon theorem state, and how is it proved?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"law","name":"Law","description":"Parallelogram law.","findings":[{"id":"law-finding","name":"Law","description":"Law.","questions":[{"text":"What is the parallelogram law in vectors and in normed spaces?","kind":"provenance"},{"text":"Which entry fits inner product spaces?","kind":"action"}]}]}]},{"id":"learn","name":"Learn","description":"Teaching and use.","layers":[{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How are parallelograms taught, and which misconceptions arise?","kind":"provenance"},{"text":"Which entry fits geometry education?","kind":"action"}]}]},{"id":"use","name":"Use","description":"Applications.","findings":[{"id":"use-finding","name":"Use","description":"Use.","questions":[{"text":"Where do parallelograms appear in design, engineering and physics?","kind":"provenance"},{"text":"Which entry fits a specific application?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Define a parallelogram and its properties.","Compute area and perimeter, showing the use of perpendicular height.","Explain special cases such as rectangles, rhombi and squares."],"mustNot":["Use side length in place of perpendicular height for area.","Assume right angles in a general parallelogram.","Ignore regional differences in how trapezoids and parallelograms are related.","Present a flawed proof as correct to a learner."],"requiresHuman":["Using computed areas for land or construction measurements that others rely on."]},"ethics":{"considerations":["Accurate maths education builds learners' confidence and skills.","Area errors in land measurement can cause disputes."],"affectedParties":["Students and learners","Teachers","Surveyors and builders"]},"owners":{"steward":"Nobody owns the concept; it is held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q130349161","type":"parent","note":"registry parent class"},{"target":"Q27678359","type":"parent","note":"registry parent class"},{"target":"Q46303","type":"parent","note":"registry parent class"},{"target":"Q47008488","type":"parent","note":"registry parent class"},{"target":"Q7135025","type":"parent","note":"registry parent class"},{"target":"Q98098837","type":"parent","note":"registry parent class"},{"target":"quadrilateral","type":"related","note":"a four-sided polygon"},{"target":"rectangle","type":"related","note":"a special case"},{"target":"trapezoid","type":"related","note":"one pair of parallel sides"},{"target":"vector addition","type":"related","note":"the parallelogram law"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.parallelogram","Wikidata: Q45867 (https://www.wikidata.org/wiki/Q45867)"]},"properties":{"applicability":"not-applicable","items":["area: base times height formula","angle sum: 360 degrees"]},"recognition":{"applicability":"optional","items":["Two pairs of parallel sides","Opposite sides equal, diagonals bisect each other","A trapezoid has one pair of parallel sides in most definitions","A four-sided figure with two pairs of parallel sides, like a slanted rectangle."]},"capabilities":{"applicability":"required","items":["state the definition and properties","compute area, perimeter and angles","classify special cases","relay classic theorems"]},"hazards":{"applicability":"required","items":["Confusing height with side length in area","Regional differences in trapezoid definitions","Assuming right angles"]},"interfaces":{"applicability":"required","items":["No regulation; definitions follow standard geometry, with regional differences in the definition of trapezoid"]},"context":{"applicability":"required","items":["A basic shape in geometry, design and engineering.","general parallelograms and rhomboids","rectangles","rhombi","squares","Varignon parallelogram of a quadrilateral","parallelograms in vector addition and physics"]}},"sources":[{"title":"Wikidata item Q45867: parallelogram","url":"https://www.wikidata.org/wiki/Q45867","note":"identity and sense of the item"},{"title":"Wikipedia: Parallelogram","url":"https://en.wikipedia.org/wiki/Parallelogram","note":"general description of the item"}],"openQuestions":["Should the Varignon parallelogram be a separate entry?","How should curriculum standards be linked?","How should definitional variation be recorded?"],"resources":{"spec":"/models/things/publications/thing-q45867/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q45867/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T21:34:02Z","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}}