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Welcome to Triangles, Theorems and Problems. Site created and maintained by Antonio
Gutierrez.
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Theorems and Problems Index,
Math Education, High School, College, Online Learning.
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Triangles, Theorems and
Problems - Table of Content
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Euclid's Elements
Book I, 23 Definitions. One-page visual illustration.
Triangles: Equilateral, Isosceles, Scalene. |
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Equilateral Triangles Index. |
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Isosceles Triangle. |
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Right Triangle. |
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Congruence.
Index.
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Similarity, Ratios, Proportions.
Index.
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Areas Index |
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Classical Theorems
of Triangles.
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Triangle Centers Index. |
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Incenter of a triangle.
Index.
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Excenter.
Index.
Excircle, Exradius.
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Centroid
/Barycenter of a triangle.
Index.
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Circumcenter of a triangle.
Index.
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Orthocenter of a triangle.
Index.
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Engineering the Impossible: Chartres Cathedral
Circle, Square, Triangle. |
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Proposed Problem 292.
Triangle, Parallel, Congruence, Similarity. |
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Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular. |
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Euclid's
Elements, Book X, Lemma for Proposition 33
One page visual illustration. |
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Proposed Problem 287:
Regular Octagon. Triangles |
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Proposed Problem 286:
Square, Midpoints, Octagon.
Triangles |
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Proposed Problem
282.
Right Triangle, Cevian, Angles, Perpendicular, Congruence. |
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Proposed Problem
281.
Triangles, Angles, Isosceles, Equilateral. |
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Proposed Problem
279.
Tangent Circles, Common External Tangent, Chords, Inradius, Triangle. |
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Proposed Problem
276.
Square, 90 degree Arcs, Circle, Radius, Triangle. |
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Proposed Problem
274.
Isosceles Triangle, 80-80-20, Angles. |
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Proposed Problem
273.
Triangle, Perpendiculars, Area of Squares. |
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Proposed Problem
270.
Tangent Circles, Common external tangent, Fractional exponents. |
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Proposed Problem
269.
Right Triangle, Altitude, Perpendicular, Projection. |
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Proposed Problem
268.
Right Triangle, Catheti and Altitude. |
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Proposed Problem
267.
Right Triangle, Product of Catheti. |
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Proposed Problem
266.
Right Triangle, Altitude, Geometric Mean. |
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Proposed Problem
265.
Right Triangle, Pythagorean Theorem. |
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Proposed Problem
264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean. |
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Proposed Problem
263.
Triangle, Median, Altitude, Orthogonal Projection, Sides. |
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Proposed Problem
260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.
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Proposed Problem
259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.
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Proposed Problem
258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem
257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem
256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.
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Proposed Problem
255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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Proposed Problem
254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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Proposed Problem
253.
Triangle, Centroid, Vertices, Distances, Squares.
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Proposed Problem
252.
Parallelogram, sides, diagonals, squares, areas.
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Proposed Problem
249.
Triangle sides, medians, squares.
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Proposed Problem
248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.
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Proposed Problem
247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon
triangle.
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Proposed Problem
246.
Napoleon's Theorem I. External Equilateral triangles. Outer Napoleon
triangle.
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Proposed Problem
245. Parallelogram with Equilateral triangles
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Proposed Problem
243. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
242. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
241. Triangle with Equilateral triangles, Congruence.
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Proposed Problem
240. Triangle with Equilateral triangles, Parallelogram.
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Proposed Problem
239. Square, Midpoints, Lines, Congruence, Pythagoras.
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Proposed Problem
238. Square, Midpoints, Lines, Congruence.
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Proposed Problem
232. Parallelogram, Line through a vertex, Perpendicular lines.
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Proposed Problem
231. Triangle, Midpoints, Transversal, Perpendicular lines.
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Proposed Problem
230. Triangle, Midpoints, Transversal, Perpendicular lines.
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Proposed Problem
229. Triangle, Centroid, Transversal, Perpendicular lines. |
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Proposed Problem
228. Triangle, Midpoints, Exterior line, Perpendiculars lines.
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Proposed Problem
227. Triangle, Centroid, Exterior line, Perpendicular lines. |
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Proposed Problem
226. Triangle, Centroid, Perpendiculars. |
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Proposed Problem
224. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Point on the extension of the base. |
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Proposed Problem
223. Viviani's theorem, Isosceles triangle,
Altitude, Distances. |
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Proposed Problem
222. Viviani's theorem, Equilateral triangle, Exterior point,
Distances. |
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Proposed Problem
221. Viviani's theorem, Equilateral triangle, Interior point,
Distances. |
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Lune of Hippocrates Index.
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Proposed Problem
220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.
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Proposed Problem
218. Right triangle, Altitude and Projections.
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Proposed Problem
217. Right triangle, Altitude and Projections.
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Proposed Problem
216. Quadrilateral, Angle Bisectors, and Concurrency.
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Journey to the Center of a Triangle (1976).
Incenter, Circumcenter, Centroid, Orthocenter.
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Congruent Triangles: SAS, SSS, ASA.
Demonstrates with animation the various relationships of angles and sides to congruency in triangles.
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Proposed Problem
213. Triangle, Incircle, Inradius, Semicircles, Common Tangents. |
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Proposed Problem
212. 120 Degree Triangle, Equilateral triangles, Areas.
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Archimedes Arbelos and Square
2.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
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Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
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Proposed Problem
211. 60 Degree Triangle, Equilateral triangles, Areas.
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Proposed Problem
210. Triangle, Angles, Auxiliary Lines.
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Proposed Problem
209. Triangle, Incircles, Inradius. |
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Proposed Problem
208. Triangle, Excircles, Angles, 360 degrees. |
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Proposed Problem
195. Area of a Triangle, Inradius, Exradii. |
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Proposed Problem
208. Triangle, Excircles, Angles, 360 degrees. |
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Proposed Problem
207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse. |
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Proposed Problem
206. Area of a Right Triangle, Inradius, andExradius relative to the hypotenuse. |
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Proposed Problem
205. Right Triangle Area, Exradii relatives to legs or catheti. |
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Proposed Problem
204. Right Triangle, Incircle, Excircles, Inradius, Exradii. |
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Proposed Problem
203. Right Triangle, Excircles, Exradii, Hypotenuse. |
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Proposed Problem
202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter. |
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Proposed Problem
201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter. |
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