Triangles, Theorems and Problems - Table of Content

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Triangles: Equilateral, Isosceles, Scalene.

Points, Theorems and Problems - Index.
non-collinear points. Triangle vertices.

Equilateral Triangles Index.

Isosceles Triangle.

Right Triangle.

Special Right Triangles.

Special Right Triangle 30-60.

Obtuse Triangle.

Altitude Index.
Theorems and Problems.

Congruence. Index.

Similarity, Ratios, Proportions. Index.

Areas Index

Classical Theorems of Triangles.

Triangle Centers Index.

Incenter of a triangle. Index.

Excenter. Index.
Excircle, Exradius.

Centroid /Barycenter of a triangle. Index.

Circumcenter of a triangle. Index.

Orthocenter of a triangle. Index.

Engineering the Impossible: Chartres Cathedral
Circle, Square, Triangle.

Kosnita's Theorem.
Circumcenters, Concurrent lines.

Routh's Theorem - Index
Triangle, Cevians, Area, Ratio.
 

Routh's Theorem 1.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 2.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 3.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 4.
Triangle, Cevians, Ratio of Areas.

Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS)

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

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

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

Proposed Problem 424.
Triangle, Cevian, Angle, 90 degree, Congruence.

Proposed Problem 423.
Triangle, 30, 40 degree, Angle, Congruence.

Proposed Problem 422.
Triangle, 24, 30 degree, Angle, Congruence.

Proposed Problem 421.
Right Triangle, Cevian, Angles, Measurement.

Proposed Problem 420.
Triangle, Altitude, Angles, Sides, Measurement.

Proposed Problem 419.
Triangle, Cevian, Incircle, Excircle, Inradius, Exradius

Proposed Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius.

Proposed Problem 416.
Triangle, Cevians, Trisectors, Area.

Proposed Problem 415.
Right Triangle, Cevian, Angles, Congruence.

Proposed Problem 414.
Triangle, Angles, Altitude, Median, Congruence.

Proposed Problem 412.
Triangle, Angles, Congruence.

Proposed Problem 411.
Triangle, Median, Angles.

Proposed Problem 410.
Two Regular Pentagons, Angle, Triangle Congruence.

Proposed Problem 409.
Quadrilateral, Diagonals, Perpendicular, Congruence, Triangle.

Proposed Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence, Triangle.

Proposed Problem 406.
Right triangle, 15 degrees, Midpoints, Congruence.

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

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.

Proposed Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Proposed Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.

Proposed Problem 397.
Triangle, Altitude, Midpoints, Congruence.

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 392.
Triangle, Parallel lines, Concurrent lines.

Proposed Problem 391.
Triangle, Parallel lines, Collinear points.

Proposed Problem 390.
Triangle, Parallel lines, Collinear points.

Proposed Problem 389.
Triangle, Parallel lines, Harmonic Mean.

Proposed Problem 388.
Triangle, Angle bisector, Perpendicular, Parallel.

Proposed Problem 387.
Triangle, Angle bisector, Perpendicular, Concyclic points.

Proposed Problem 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter, Congruence.

Proposed Problem 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Proposed Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Proposed Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

Proposed Problem 377.
Triangle, Internal Angle Bisector, Altitude.

Proposed Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

Proposed Problem 375.
Triangle, Excenter, External Angle Bisectors.

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

Proposed Problem 371.
Square, Inscribed circle, Triangle, Area.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Proposed Problem 368.
Triangle, 120 degrees, Angle bisectors, Perpendicular.

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.

Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Curvilinear triangle, Area.

Proposed Problem 363.
Right triangle, Congruence, Angles.

Proposed Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle.

Proposed Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters.

Proposed Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence.

Proposed Problem 357.
Square, Exterior point, Triangles, Area.

Proposed Problem 356.
Square, Point inside, Triangles, Area.

Proposed Problem 350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles.

Proposed Problem 349.
Triangle, Cevian, Incircles, Tangents, Tangency Point.

Proposed Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points.

Proposed Problem 341.
Triangle, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 340.
Triangle, Angle Bisectors, Perpendiculars, Distances. Exterior Point.

Proposed Problem 339.
Triangle, Angle Bisectors, Perpendiculars, Distances. Interior Point.

Proposed Problem 338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points.

Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points.

Proposed Problem 328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint.

Proposed Problem 326.
Equilateral triangle, Semicircle, Equal arcs.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Proposed Problem 321.
Triangle, Incenter, Excircle, Midpoint of the Altitude, Collinearity.

Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points.

Proposed Problem 319.
Triangle, Altitudes, Perpendiculars, Collinear points.

Proposed Problem 318.
A Scalene triangle, Altitudes, Collinear points.

Proposed Problem 317.
Right triangle and Inscribed Squares.

Proposed Problem 292.
Triangle, Parallel, Congruence, Similarity.

Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular.

Euclid's Elements, Book X, Lemma for Proposition 33
One page visual illustration.

Proposed Problem 287: Regular Octagon. Triangles

Proposed Problem 286: Square, Midpoints, Octagon.
Triangles

Proposed Problem 282.
Right Triangle, Cevian, Angles, Perpendicular, Congruence.

Proposed Problem 281.
Triangles, Angles, Isosceles, Equilateral.

Proposed Problem 279.
Tangent Circles, Common External Tangent, Chords, Inradius, Triangle.

Proposed Problem 276.
Square, 90 degree Arcs, Circle, Radius, Triangle.

Proposed Problem 274.
Isosceles Triangle, 80-80-20, Angles.

Proposed Problem 273.
Triangle, Perpendiculars, Area of Squares.

Proposed Problem 270.
Tangent Circles, Common external tangent, Fractional exponents.

Proposed Problem 269.
Right Triangle, Altitude, Perpendicular, Projection.

Proposed Problem 268.
Right Triangle, Catheti and Altitude.

Proposed Problem 267.
Right Triangle, Product of Catheti.

Proposed Problem 266.
Right Triangle, Altitude, Geometric Mean.

Proposed Problem 265.
Right Triangle, Pythagorean Theorem.

Proposed Problem 264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean.

Proposed Problem 263.
Triangle, Median, Altitude, Orthogonal Projection, Sides.

Proposed Problem 260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.

Proposed Problem 259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.

Proposed Problem 258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Proposed Problem 257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Proposed Problem 256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.

Proposed Problem 255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.

Proposed Problem 254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.

Proposed Problem 253.
Triangle, Centroid, Vertices, Distances, Squares.

Proposed Problem 252.
Parallelogram, sides, diagonals, squares, areas.

Proposed Problem 249.
Triangle sides, medians, squares.

Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

Proposed Problem 247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon triangle.

Proposed Problem 246.
Napoleon's Theorem I. External Equilateral triangles. Outer Napoleon triangle.

Proposed Problem 245. Parallelogram with Equilateral triangles  

Proposed Problem 243. Triangle with Equilateral triangles, Parallelogram.  

Proposed Problem 242. Triangle with Equilateral triangles, Parallelogram.  

Proposed Problem 241. Triangle with Equilateral triangles, Congruence.  

Proposed Problem 240. Triangle with Equilateral triangles, Parallelogram.  

Proposed Problem 239. Square, Midpoints, Lines, Congruence, Pythagoras.  

Proposed Problem 238. Square, Midpoints, Lines, Congruence.  

Proposed Problem 232. Parallelogram, Line through a vertex, Perpendicular lines.  

Proposed Problem 231. Triangle, Midpoints, Transversal, Perpendicular lines.  

Proposed Problem 230. Triangle, Midpoints, Transversal, Perpendicular lines.  

Proposed Problem 229. Triangle, Centroid, Transversal, Perpendicular lines.  

Proposed Problem 228. Triangle, Midpoints, Exterior line, Perpendiculars lines.  

Proposed Problem 227. Triangle, Centroid, Exterior line, Perpendicular lines.  

Proposed Problem 226. Triangle, Centroid, Perpendiculars.  

Proposed Problem 224. Viviani's theorem, Isosceles triangle, Altitude, Distances, Point on the extension of the base.  

Proposed Problem 223. Viviani's theorem, Isosceles triangle, Altitude, Distances.  

Proposed Problem 222. Viviani's theorem, Equilateral triangle, Exterior point, Distances.  

Proposed Problem 221. Viviani's theorem, Equilateral triangle, Interior point, Distances.  

Lune of Hippocrates Index.

Proposed Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.

Proposed Problem 218. Right triangle, Altitude and Projections.

Proposed Problem 217. Right triangle, Altitude and Projections.

Proposed Problem 216. Quadrilateral, Angle Bisectors, and Concurrency.

Journey to the Center of a Triangle (1976). Incenter, Circumcenter, Centroid, Orthocenter.

Congruent Triangles: SAS, SSS, ASA. Demonstrates with animation the various relationships of angles and sides to congruency in triangles.

Proposed Problem 213. Triangle, Incircle, Inradius, Semicircles, Common Tangents.

Proposed Problem 212. 120 Degree Triangle, Equilateral triangles, Areas.

Archimedes Arbelos and Square 2. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation.

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation.

Proposed Problem 211. 60 Degree Triangle, Equilateral triangles, Areas.

Proposed Problem 210. Triangle, Angles, Auxiliary Lines.

Proposed Problem 209. Triangle, Incircles, Inradius.  

Proposed Problem 208. Triangle, Excircles, Angles, 360 degrees.  

Proposed Problem 195. Area of a Triangle, Inradius, Exradii.  

Proposed Problem 208. Triangle, Excircles, Angles, 360 degrees.  

Proposed Problem 207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse.  

Proposed Problem 206. Area of a Right Triangle, Inradius, andExradius relative to the hypotenuse.  

Proposed Problem 205. Right Triangle Area, Exradii relatives to legs or catheti.  

Proposed Problem 204. Right Triangle, Incircle, Excircles, Inradius, Exradii.  

Proposed Problem 203. Right Triangle, Excircles, Exradii, Hypotenuse.  

Proposed Problem 202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter.  

Proposed Problem 201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter.