Online Geometry: Equilateral Triangles, Theorems and Problems  Page 1




Euclid's Elements
Book I, 23 Definitions. Onepage visual illustration.
Equilateral triangle. 

Euclid's Elements Book I, Proposition 3: Given two unequal straight
lines, to cut off from the greater a straight line equal to the less.
Equilateral triangle. 

Euclid's Elements Book I, Proposition 2: To place at a given point (as
an extremity) a straight line equal to a given straight line.
Equilateral triangle. 

Euclid's Elements Book I, Proposition 1: On a given finite line to
construct an equilateral triangle 

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

Napoleon's
theorems and problems, Index.
Equilateral triangle. 

Geometry Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines. 

Da Vinci Tetrahedron and Jenn 3D tool for visualizing
Coxeter polytopes.
Jenn 3D is a free software license program for visualizing
regular polytopes in stereographic projection. 

Da Vinci Octahedron and Jenn 3D tool for visualizing Coxeter
polytopes.
Jenn 3D is a free software license program for visualizing
regular polytopes in stereographic projection. 

Da Vinci Icosahedron and Jenn 3D tool for visualizing
Coxeter polytopes.
Jenn 3D is a free software license program for visualizing
regular polytopes in stereographic projection. 

Optical Prism with Equilateral Triangle Form.
Scene created using Prism HD for iPad. 

Second Fermat Point: Static diagram.
Second Fermat Point: Dynamic diagram.
Triangle, Equilateral triangles, Concurrent lines, GeoGebra, HTML5 Animation for Tablets (iPad, Nexus) 

Lester Circle Theorem.
Equilateral Triangle. 

Geometry Problem 1577:
Prove that in triangle ABC, segment AB equals the sum of segments BD and CD, with given angles and congruent segments. 

Geometry Problem 1566:
Demonstrate AC Equals AE + CD in an Equilateral Triangle ABC Involving Cevians and 60 Degrees.. 

Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle. 

Geometry Problem 1557:
Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral,
isosceles, midpoint and congruence 

Geometry
Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 1005030 Degree Angles and Cevian Lengths  A High School Challenge.
. 

Geometry
Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. 

Geometry
Problem 1516 and a Thematic Poem.
Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths. Difficulty Level: High School. 

Geometry
Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School. 

Geometry
Problem 1504.
Squares, Equilateral Triangle, Parallel, Angle. 

Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra. 

Geometry Problem 1434.
Equilateral Triangle, Tangent Circles, Tangent Lines, Arithmetic Mean, Measurement,
Poster, Typography, iPad Apps. 

Geometry Problem 1406. Four Congruent Circles, Measurement, Metric Relations,
Sum of the Squares. 

Geometry Problem 1405. Four Congruent Circles, Congruent Chords. 

Geometry Problem 1372. Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude, Sketch, iPad Apps. 

Geometry Problem 1362.
Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps. 

Geometry Problem 1348. Three Concentric Circles, Equilateral Triangle, Perpendicular Bisector, Congruence. 

Geometry Problem 1347. Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle. 

Geometry Problem 1346. Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance. 

Geometry Problem 1345: Three Equilateral Triangles, Center, Area, Common Vertex. 

Geometry Problem 1323.
Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 3060 degrees. 

Geometry Problem 1319.
Hexagons, Equilateral Triangles, Center, Midpoints. 

Geometry Problem 1318.
Rectangle, Equilateral Triangle, Distances, Perpendicular, Measurement. 

Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence. 

Geometry Problem 1313.
Regular Decagon, Pentadecagon, Equilateral Triangle, Congruence. 

Geometry Problem 1284.
Two Equilateral Triangle, Midpoint, Congruence. 

Geometry Problem 1283.
Two Equilateral Triangle, Perpendicular, Midpoint. 

Geometry Problem 1277.
Equilateral Triangle, Circumcircle, Externally Tangent Circles, Tangent Line, Measurement. 

Geometry Problem 1276.
Equilateral Triangle, Circumcircle, Internally Tangent Circles, Tangent Line, Measurement. 

Geometry Problem 1275.
Equilateral Triangle, Perpendicular, Projection, Metric Relations, Measurement. 

Geometry Problem 1238
Square, Equilateral Triangle, Metric Relations. Mobile Apps. 

Geometry Problem 1234
Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points. 

Geometry Problem 1230
Quadrilateral, 60 Degrees, Congruence, Metric Relations. 

Geometry Problem 1225
Equilateral Triangle, Circumcircle, Angle Bisector, Congruence. 

Geometry Problem 1220
Equilateral Triangles, Midpoints, 60 Degrees, Congruence. 

Geometry Problem 1219
Equilateral Triangles, Midpoints, 60 Degrees, Congruence, Rhombus. 

Geometry Problem 1218
Triangle, Equilateral Triangles, Midpoints. 

Geometry Problem 1212
Equilateral Triangle, Equilateral Hexagon, Concurrent Lines. 

Geometry Problem 1205
Triangle, Centroid, Outer and Inner Napoleon Equilateral Triangles. 

Geometry Problem 1199
Equilateral Triangle, Square, Altitude, Circle, Incircle, Inradius, Metric Relations. 

Geometry Problem 1194
Equilateral Triangle, Perpendicular, Distance, Side, Metric Relations. 

Geometry Problem 1161.
Scalene Triangle, 60 Degrees, Angle, Orthocenter, Circumcenter, Equilateral Triangle, Congruence. 

Geometry Problem 1147.
Scalene Triangle, Orthocenter, Circumcenter, Congruence, Equilateral Triangle. 

Geometry Problem 1126.
Equilateral Triangle, Circumcircle, Metric Relation, Harmonic Mean. 

Geometry Problem 1125.
Triangle, Four Equilateral Triangles, Centroid, Midpoint. 

Geometry Problem
1120.
Isosceles Right Triangle, 120 Degree, Angle, Equilateral, Metric Relations. 

Geometry Problem
1115.
Right Triangle, Angle Trisection, Equilateral Triangle. 

Geometry Problem
1092.
Equilateral Triangle, Square, Circle, Tangent, 90 Degree, Sangaku. 