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Cevian

In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. Medians, symmedians, angle bisectors, altitudes are all special cases of cevians. The name cevian comes from the Italian mathematician Giovanni Ceva, who proved a theorem about cevians which also bears his name.

Length, Splitter & Angle trisectors

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Length

Stewart's theoremMnemonicMedianSemiperimeterPerpendicular
5 related topics

Splitter

SplitterPerimeterConcurNagel point
4 related topics

Angle trisectors

TrisectEquilateral triangleMorley triangle
3 related topics

Ratio properties

Identity
1 related topics

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Overview

Length

Ratio properties

Splitter

Angle trisectors

Area of inner triangle formed by cevians

Advanced semantic analysis

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Map overview Semantic statistics

Cevian

Nodes31
Edges30
Triples38
Avg. degree1.94
Density0.064516
Components1

How this topic connects Entity context

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Cevian

Top relations

related to References · 22
Cevian → Allyn, America, American Mathematical Monthly, BaconRoss Honsberger, Episodes, Eves, Geometry, Howard, Indika Shameera Amarasinghe, Journal, Mathematical Association, National Mathematics Competitions, New Theorem, Nineteenth, One, Right-angled Cevian Triangle, Some, Survey, Twentieth Century Euclidean Geometry, Vladimir Karapetoff
related to Ratio properties · 4
Cevian → Ceva's, Referring, The, There
related to Stewart's theorem · 3
Cevian → Less, Stewart's, The
related to Angle trisectors · 2
Cevian → If, Morley
related to Splitter · 2
Cevian → Nagel, The
is a · 1
Cevian → line segment which joins a vertex of a triangle to a point on the opposite side of the triangle
related to Altitude · 1
Cevian → If
related to Angle bisector · 1
Cevian → If
related to Area of inner triangle formed by cevians · 1
Cevian → Routh's
related to Median · 1
Cevian → If

Important terminology Word statistics

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Important terminology

triangle theorem cevians point side angle vertex three length properties bisectors also geometry medians area formed happens opposite median altitude

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cevianis aline segment which joins a vertex of a triangle to a point on the opposite side of the triangle0.90text
Cevianrelated to AltitudeIf0.60section
Cevianrelated to Angle bisectorIf0.60section
Cevianrelated to Angle trisectorsIf0.60section
Cevianrelated to Angle trisectorsMorley0.60section
Cevianrelated to Area of inner triangle formed by ceviansRouth's0.60section
Cevianrelated to MedianIf0.60section
Cevianrelated to Ratio propertiesThere0.60section
Cevianrelated to Ratio propertiesReferring0.60section
Cevianrelated to Ratio propertiesThe0.60section
Cevianrelated to Ratio propertiesCeva's0.60section
Cevianrelated to ReferencesEves0.60section

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