College Geometry Online, eLearning

Online Geometry: Classical Theorems of Euclidean Geometry

Classical Theorems - Page 1

Euclidean Geometry

 

Dynamic Geometry 1452

Dynamic Geometry 1452.
Japanese Theorem, Sangaku, Cyclic Quadrilateral, Incenter, Rectangle, Inradius. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1451

Dynamic Geometry 1451.
Orthopole of a Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1450

Dynamic Geometry 1450.
Ortholine, Steiner Line, Complete Quadrilateral, Collineal Orthocenters. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1449

Dynamic Geometry 1449.
Salmon Line. Step-by-step illustration using GeoGebra.

Dynamic Geometry 1448

Dynamic Geometry 1448.
Simson Line. Step-by-step illustration using GeoGebra.

Problem 1447

Dynamic Geometry Problem 1447.
Outer Vecten Point. Step-by-step illustration using GeoGebra.

Problem 1446

Dynamic Geometry Problem 1446.
Lemoine Line, triangle, circumcircle, tangent, collinear points. Step-by-step animation using GeoGebra.

Problem 1444

Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Step-by-step animation using GeoGebra.

Classical Pythagorean Theorem

Pythagorean Theorem.

Euclid's Elements, Book II, Proposition 12

Euclid's Elements Book II, Proposition 12: Law of Cosines.

Euclid's Elements: Book II, Proposition 13: Law of Cosines

Euclid's Elements Book II, Proposition 13: Law of Cosines.

Median Length theorem

Median length, Apollonius' Theorem

Pythagoras Theorem, 47th Proposition of Euclid's Book I

The significance of the Pythagorean theorem by Jacob Bronowski.
Pythagorean Theorem, 47th Proposition of Euclid's Book I.

Geometry Problem 889

Carnot's Theorem. Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets.

Ceva's Theorem

Ceva's Theorem. Concurrency. Interactive proof with animation. Key concept: Menelaus Theorem. 

Menelaus Theorem 

Menelaus' Theorem. Interactive proof with animation and key concepts..

 

van Aubel theorem

van Aubel's Theorem. Quadrilateral with Squares. Proof with animation.

van Aubel theorem for Tablets, iPad, Nexus, Galaxy

van Aubel's Theorem. Quadrilateral with Squares. Proof with animation for Tablets, iPad, Nexus, Galaxy.

Problem 1445

Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra.

Heron's Formula.
Key facts and
a purely geometric step-by-step proof.
 

Euclid's Elements 23 definitions

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Angle Bisector Theorem

Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem

Euclid's Elements Book XIII, Proposition 10

Euclid's Elements, Book XIII, Proposition 10 One page visual illustration.

Ptolemy's Theorem.
 

Brahmagupta's Theorem

Dynamic Geometry: Brahmagupta Theorem, . GeoGebra, HTML5 Animation for Tablets

Brianchon Theorem

Brianchon's Theorem in a Circumscribed Hexagon.

Brianchon Corollary

Brianchon Corollary, Circumscribed Hexagon, Concurrency lines.

Carnot's Theorem, Acute Triangle

Carnot's Theorem in an Acute Triangle.

Carnot's Theorem, Obtuse Triangle

Carnot's Theorem in an Obtuse Triangle.

Clifford's theorem

Clifford's Circle Chain Theorems. This is a step by step presentation of the first theorem. Clifford discovered, in the ordinary Euclidean plane, a "sequence or chain of theorems" of increasing complexity, each building on the last in a natural progression.
 

Cyclic Quadrilateral: Ratio of the Diagonals
 

Euler Line, Nine Point Circle

Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.

Soddy Circles and Descartes Theorem

Soddy Circles and Descartes Theorem.
Three tangent circles, Inscribed and Circumscribed Circles, Radii.

Elearning 155

Euler's Problem, Problem 155. Distance between the Incenter to the Circumcenter.

The Simson Line Index

The Simson Line, Theorems and Problems - Index.

Casey Theorem

Casey's Theorem. Generalized Ptolemy's Theorem.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

Brahmagupta's Theorem Cyclic quadrilateral.

Platonic Solids, Interactive animation.
HTML5 Animation for iPad and Nexus
Flash Animation.

Theaetetus Theorem, Platonic Solids

Theaetetus' Theorem, Platonic Solids, Interactive animation

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Last updated: Dec 10, 2019