Online Geometry: Equilateral Triangles, Theorems and Problems - Page 1
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![Equilateral triangles](equilateral_triangle_17_ind.jpg) |
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![Euclid's Elements 23 definitions](euclid_elements_definition_170.jpg) |
Euclid's Elements
Book I, 23 Definitions. One-page visual illustration.
Equilateral triangle. |
![Euclid's Elements Book I, Proposition 3](euclid_book_i_3_17.jpg) |
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](euclid_book_i_2_17.jpg) |
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](euclid_book_i_1_17.jpg) |
Euclid's Elements Book I, Proposition 1: On a given finite line to
construct an equilateral triangle |
![Euclid's Elements Book XIII, Proposition 10](euclid_elements_book_xiii_10_17.jpg) |
Euclid's
Elements, Book XIII, Proposition 10 One page visual illustration. |
![Napoleon Theorem and Problem Index](napoleon_theorem_index_17.jpg) |
Napoleon's
theorems and problems, Index.
Equilateral triangle. |
![Equilateral triangles](../problem/p404_equilateral_triangle_1.jpg) |
Geometry Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines. |
![Da Vinci Tetrahedron Jenn 3D Coxeter polytopes](../solid/da_vinci_tetrahedron_jenn_1.jpg) |
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, Jenn3D](../solid/da_vinci_octahedron_jenn_17.jpg) |
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, Jenn3D](../solid/da_vinci_icosahedron_jenn_1.jpg) |
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](../ipad/prism-hd/prism-hd-ipad-equilateral-triangle-optics-light-1.jpg) |
Optical Prism with Equilateral Triangle Form.
Scene created using Prism HD for iPad. |
![Second Fermat Point](../center/fermat-point-second-dynamic-triangle-equilateral-1.jpg) |
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](../circle/lester-circle-fermat-circumcenter-nine-point-college-1.jpg) |
Lester Circle Theorem.
Equilateral Triangle. |
![Geometry Problem 1566](../school-college/6/p1566-equilateral-triangle-cevian-60-degrees-mystery-sum-of-segments-tutoring-1.jpg) |
Geometry Problem 1566:
Demonstrate AC Equals AE + CD in an Equilateral Triangle ABC Involving Cevians and 60 Degrees.. |
![Geometry Problem 1558](../school-college/6/p1558-midpoints-of-segments-connecting-corresponding-vertices-of-two-equilateral-triangles-form-an-equilateral-triangle-1.jpg) |
Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle. |
![Geometry Problem 1557](../school-college/6/p1557-right-triangle-equilateral-isosceles-congruence-midpoint-angle-problem-solving-1.jpg) |
Geometry Problem 1557:
Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral,
isosceles, midpoint and congruence |
![Geometry Problem 1529](../school-college/6/p1529-triangle-interior-cevian-30-100-degree-congruence-find-missing-angle-1.jpg) |
Geometry
Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths - A High School Challenge.
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![Geometry Problem 1525](../school-college/6/p1525-right-triangle-equilateral-midpoint-hypotenuse-distance-1.jpg) |
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](../school-college/6/p1516-solving-for-the-length-of-a-side-in-an-equiangular-hexagon-1.jpg) |
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](../school-college/6/p1508-isosceles-equilateral-triangle-angles-quadrilateral-60-80-degrees-1.jpg) |
Geometry
Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School. |
![Geometry Problem 1504](../school-college/6/p1504-3-squares-equilateral-triangle-angle-parallel-1.jpg) |
Geometry
Problem 1504.
Squares, Equilateral Triangle, Parallel, Angle. |
![Problem 1444](../school-college/5/p1444-asymmetric-propeller-equilateral-triangle-geogebra-1.jpg) |
Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra. |
![Problem 1434](../school-college/5/p1434-equilateral-triangle-tangent-circles-line-1.jpg) |
Geometry Problem 1434.
Equilateral Triangle, Tangent Circles, Tangent Lines, Arithmetic Mean, Measurement,
Poster, Typography, iPad Apps. |
![Problem 1406](../school-college/5/p1406-four-congruent-circles-measurement-tutor-1.jpg) |
Geometry Problem 1406. Four Congruent Circles, Measurement, Metric Relations,
Sum of the Squares. |
![Problem 1405](../school-college/5/p1405-four-congruent-circles-chords-tutor-1.jpg) |
Geometry Problem 1405. Four Congruent Circles, Congruent Chords. |
![Problem 1372 Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude](../school-college/4/p1372-equilateral-triangle-exterior-cevian-inradius-exradius-altitude-1.jpg) |
Geometry Problem 1372. Equilateral Triangle, Exterior Cevian, Inradius, Exradius, Altitude, Sketch, iPad Apps. |
![Geometry problem 1362](../school-college/4/p1362-equilateral-triangle-inscribed-circle-lunula-area-1.jpg) |
Geometry Problem 1362.
Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps. |
![Geometry problem 1348](../school-college/4/p1348-concentric-circles-equilateral-triangle-tutoring-1.jpg) |
Geometry Problem 1348. Three Concentric Circles, Equilateral Triangle, Perpendicular Bisector, Congruence. |
![Geometry problem 1347](../school-college/4/p1347-equilateral-triangle-bisector-circle-tangent-tutoring-1.jpg) |
Geometry Problem 1347. Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle. |
![Geometry problem 1346](../school-college/4/p1346-equilateral-triangle-incircle-altitude-tutoring-1.jpg) |
Geometry Problem 1346. Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance. |
![Geometry problem 1345](../school-college/4/p1345-equilateral-triangle-common-vertex-center-area-1.jpg) |
Geometry Problem 1345: Three Equilateral Triangles, Center, Area, Common Vertex. |
![Geometry problem 1323](../school-college/4/p1323-square-equilateral-triangle-dodecagon-1.jpg) |
Geometry Problem 1323.
Square, Angle Trisector, Diagonal, Regular Dodecagon, Area, 30-60 degrees. |
![Geometry problem 1319](../school-college/4/p1319-hexagon-square-midpoint-equilateral-triangle-1.jpg) |
Geometry Problem 1319.
Hexagons, Equilateral Triangles, Center, Midpoints. |
![Geometry problem 1318](../school-college/4/p1318-equilateral-triangle-rectangle-common-vertex-distances-1.jpg) |
Geometry Problem 1318.
Rectangle, Equilateral Triangle, Distances, Perpendicular, Measurement. |
![Geometry problem 1314](../school-college/4/p1314-equilateral-triangle-incircle-tangent-congruence-1.jpg) |
Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence. |
![Geometry problem 1313](../school-college/4/p1313-decagon-pentadecagon-equilateral-triangle-1.jpg) |
Geometry Problem 1313.
Regular Decagon, Pentadecagon, Equilateral Triangle, Congruence. |
![Geometry problem 1284](../school-college/3/p1284-equilateral-triangle-midpoint-1.jpg) |
Geometry Problem 1284.
Two Equilateral Triangle, Midpoint, Congruence. |
![Geometry problem 1283](../school-college/3/p1283-equilateral-triangle-midpoint-perperpendicular-1.jpg) |
Geometry Problem 1283.
Two Equilateral Triangle, Perpendicular, Midpoint. |
![Geometry problem 1277](../school-college/3/p1277-equilateral-triangle-externally-tangent-circle-tutoring-1.jpg) |
Geometry Problem 1277.
Equilateral Triangle, Circumcircle, Externally Tangent Circles, Tangent Line, Measurement. |
![Geometry problem 1276](../school-college/3/p1276-equilateral-triangle-internally-tangent-circle-tutoring-1.jpg) |
Geometry Problem 1276.
Equilateral Triangle, Circumcircle, Internally Tangent Circles, Tangent Line, Measurement. |
![Geometry problem 1275](../school-college/3/p1275-equilateral-triangle-projection-measure-1.jpg) |
Geometry Problem 1275.
Equilateral Triangle, Perpendicular, Projection, Metric Relations, Measurement. |
![Geometry problem 1238](../school-college/3/p1238-square-equilateral-triangle-metric-relation-mobile-apps-1.jpg) |
Geometry Problem 1238
Square, Equilateral Triangle, Metric Relations. Mobile Apps. |
![Geometry problem 1234](../school-college/3/p1234-quadrilateral-60-degrees-cyclic-concyclic-midpoint-1.jpg) |
Geometry Problem 1234
Quadrilateral, 60 Degrees, Midpoint, Congruence, Cyclic Quadrilateral, Concyclic Points. |
![Geometry problem 1230](../school-college/3/p1230-quadrilateral-equilateral-triangle-metric-relations-1.jpg) |
Geometry Problem 1230
Quadrilateral, 60 Degrees, Congruence, Metric Relations. |
![Geometry problem 1225](../school-college/3/p1225-equilateral-triangle-bisector-circle-congruence-1.jpg) |
Geometry Problem 1225
Equilateral Triangle, Circumcircle, Angle Bisector, Congruence. |
![Geometry problem 1220](../school-college/3/p1220-scalene-equilateral-triangles-midpoint-class-1.jpg) |
Geometry Problem 1220
Equilateral Triangles, Midpoints, 60 Degrees, Congruence. |
![Geometry problem 1219](../school-college/3/p1219-equilateral-triangles-midpoint-rhombus-tutor-1.jpg) |
Geometry Problem 1219
Equilateral Triangles, Midpoints, 60 Degrees, Congruence, Rhombus. |
![Geometry problem 1218](../school-college/3/p1218-scalene-equilateral-triangles-midpoint-tutor-1.jpg) |
Geometry Problem 1218
Triangle, Equilateral Triangles, Midpoints. |
![Geometry problem 1212](../school-college/3/p1212-equilateral-triangle-inscribed-hexagon-concurrency-1.jpg) |
Geometry Problem 1212
Equilateral Triangle, Equilateral Hexagon, Concurrent Lines. |
![Geometry problem 1205](../school-college/3/p1205-napoleon-theorem-inner-outer-centroid-1.jpg) |
Geometry Problem 1205
Triangle, Centroid, Outer and Inner Napoleon Equilateral Triangles. |
![Geometry problem 1199](../school-college/2/p1199-square-equilateral-triangle-circle-metric-relation-1.jpg) |
Geometry Problem 1199
Equilateral Triangle, Square, Altitude, Circle, Incircle, Inradius, Metric Relations. |
![Geometry problem 1194](../school-college/2/p1194-equilateral-triangle-parallel-perpendicular-metric-relations-1.jpg) |
Geometry Problem 1194
Equilateral Triangle, Perpendicular, Distance, Side, Metric Relations. |
![Geometry problem 1161](../school-college/2/p1161-scalene-triangle-60-degrees-orthocenter-circumcenter-1.jpg) |
Geometry Problem 1161.
Scalene Triangle, 60 Degrees, Angle, Orthocenter, Circumcenter, Equilateral Triangle, Congruence. |
![Geometry problem 1147](../school-college/2/p1147-triangle-orthocenter-circumcenter-congruence-equilateral-1.jpg) |
Geometry Problem 1147.
Scalene Triangle, Orthocenter, Circumcenter, Congruence, Equilateral Triangle. |
![Geometry problem 1126](../school-college/2/p1126-equilateral-triangle-circumcircle-harmonic-mean-1.jpg) |
Geometry Problem 1126.
Equilateral Triangle, Circumcircle, Metric Relation, Harmonic Mean. |
![Geometry problem 1125](../school-college/2/p1125-triangle-four-equilateral-centroid-midpoint-1.jpg) |
Geometry Problem 1125.
Triangle, Four Equilateral Triangles, Centroid, Midpoint. |
![Geometry Problem 1120](../school-college/2/p1120-isosceles-right-triangle-equilateral-metric-relation-math-1.jpg) |
Geometry Problem
1120.
Isosceles Right Triangle, 120 Degree, Angle, Equilateral, Metric Relations. |
![Geometry Problem 1115](../school-college/2/p1115-right-triangle-angle-trisector-equilateral-math-1.jpg) |
Geometry Problem
1115.
Right Triangle, Angle Trisection, Equilateral Triangle. |
![Geometry Problem 1092](../school-college/1/p1092-right-equilateral-triangle-square-circle-tangent-sangaku-class-math-1.jpg) |
Geometry Problem
1092.
Equilateral Triangle, Square, Circle, Tangent, 90 Degree, Sangaku. |