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geometric mean theorem

theorem that, in a right triangle, the altitude equals the geometric mean of the the two line segments on the hypotenuse created by the altitude
Intangible theorem Q2226868

Facts

6 properties
Instance of
theorem
Part of
list of theorems, Pythagoras–Euclid theorems[5][6]
Defining formula
h=\sqrt{pq}
Maintained by WikiProject
WikiProject Mathematics[8]
Named after
Euclid, geometric mean, altitude[2][3][4]
Statement describes
right triangle[7]
🏷️ Also known as
en geometric mean theorem en Euclid's second theorem en right triangle altitude theorem ar مبرهنة الوسط الهندسي cs Eukleidova věta o výšce cs Eukleidova věta o výšce pravoúhlého trojúhelníka de Höhensatz des Euklid de Höhensatz es teorema de la altura de un triángulo rectángulo es teorema de la media geométrica fi Geometrisen keskiarvon lause fr théorème de la moyenne géométrique hi गुणोत्तर माध्य प्रमेय it teorema dell'altezza di Euclide it secondo teorema di Euclide ja 幾何平均定理 nl hoogtelijn nl hoogtelijnstelling nl hoogtelijnstelling van Euclides nl hoogtelijn van Euclides
🔖 Identifiers · 4
Image (Wikimedia Commons)
Hoehensatz2.svg ↗
Freebase ID
/m/0pb4mvs
Google Knowledge Graph ID
/g/121n3_d1
Microsoft Academic ID (discontinued)
187609146

Report an error or request removal Lineage (PROV-JSON)

🔗 Connections
Named after 3
Euclid, geometric mean, altitude
Instance of 1
theorem
Maintained by WikiProject 1
WikiProject Mathematics
Part of 1
list of theorems
Statement describes 1
right triangle
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Summary

geometric mean theorem is a theorem[1].

Related Entities

Euclid

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.
  6. [7] ↑ . wikidata.org.
  7. [8] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

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APA 4ort.xyz Knowledge Graph. (2026). geometric mean theorem. Retrieved November 3, 2026, from https://4ort.xyz/entity/geometric-mean-theorem
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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 12d ago · Estopedist1 · 2026-10-23 view diff on Wikidata ↗
    Named after → —
    Named after → Euclid, geometric mean, altitude
    Part of → list of theorems, Pythagoras–Euclid theorems
    Statement describes → right triangle
    + 7 other properties edited (see Wikidata diff for full list)
    "/* wbmergeitems-from:0||Q12362438 */"
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