Online Geometry: Triangles, Theorems and Problems

Triangles Theorems and Problems- Table of Content

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

Triangles and Lissajous Art

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

Equilateral Triangles Index.

Isosceles Triangle.

Isosceles Triangle 80-20-80. Index.

Right Triangle.

Special Right Triangles.

Special Right Triangle 30-60.

Obtuse Triangle.

Altitude Index.
Theorems and Problems.

Semiperimeter, Perimeter 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.

Circumcircle Index.

Triangle Incenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Triangle Orthocenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Triangle Centroid by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Triangle Circumcenter by Folding, Video.
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Napoleon's theorems and problems, Index.

The Simson Line, Theorems and Problems - Index.

Triangle Geometry in the Real World, New York - Slideshow.

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

Kosnita's Theorem.
Circumcenters, Concurrent lines.

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

Marion Walter's Theorem and Related Topics: Index

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 7
Given two straight lines constructed on a straight line (from its extremities) and meeting in a point,...

Euclid's Elements Book I, Proposition 8: (Side-Side-Side SSS Congruence)

Euclid's Elements Book I, Proposition 5: (Pons Asinorum) Isosceles triangles

Euclid's Elements Book I, Proposition 6: Converse of I.5

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

Carnot's Theorem in an Acute Triangle.

Carnot's Theorem in an Obtuse Triangle.

Geometry Problem 726.
Isosceles Triangle, Perpendicular, Midpoint, 90 Degrees.

Geometry Problem 721.
Triangle, Orthocenter, Circumcircle, Altitude, Collinear points.

Geometry Problem 715.
Triangle, Altitudes, Parallel, Circumcircle, Angle, Measurement.

Geometry Problem 714.
Triangle, Parallel, Cevians, Midpoints, Median, Ceva Theorem.

Geometry Problem 713.
Tangent Circles, Diameter, Chord, Tangent, Incenter, Incircle, Triangle.

Geometry Problem 712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure, Triangle.

Geometry Problem 711.
Rectangle, Midpoint, Angle, Concyclic Points, Cyclic Quadrilateral.

Geometry Problem 710.
Parallelogram, Midpoint, Diagonal, Collinear Points, Metric Relations, Triangle, Similarity, Congruence.

Geometry Problem 709.
Parallelogram, Midpoint, Diagonal, Metric Relations, Triangle.

Geometry Problem 707.
Triangle, Excenters, Angle Bisectors, Angle, Measurement.

Geometry Problem 706.
Triangle, Cevian, Three Circumcenters, Circumcircles, Concyclic Points, Cyclic quadrilateral.

Geometry Problem 704.
Triangle, Orthocenter, Altitude, Midpoint, Perpendicular.

Geometry Problem 703.
Triangle, Incircle, Tangency point, Diameter, Congruence.

Geometry Problem 702.
Triangle, Circumcircle, Parallel, Concyclic Points.

Geometry Problem 700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of a side, Metric Relations.

Geometry Problem 699.
Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations.

Geometry Problem 698.
Quadrilateral, Diagonal, Angle Bisector, Triangle, 120 Degrees.

Geometry Problem 697.
Square, Circle, Sector, Segment, Tangent, Inscribed, Congruence, Mind Map, Polya.

Geometry Problem 696.
Triangle, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Geometry Problem 695.
Triangle, Angles, Auxiliary Construction, Congruence, Mind Map, Polya.

Geometry Problem 694.
Triangle, Angles, 30 Degrees, Auxiliary Construction, Mind Map, Polya.

Geometry Problem 691.
Isosceles Triangle, 80-80-20 Degrees, Angles, Congruence, Mind Map, Polya.

Problem 690: Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.

Geometry Problem 689.
Triangle, Three Excircles, Tangency points, Tangent lines, Concurrent Lines, Mind Map.

Geometry Problem 688.
Triangle, Angles, 10, 20, 30, 40, 60 Degrees, Measure, Mind Map, Polya.

Geometry Problem 687.
Triangle, Three Excircles, Tangency points, Concurrent Lines.

Geometry Problem 686.
Triangle, Three Excircles, Tangency points, Tangent lines, Semi-perimeter, Congruence.

Geometry Problem 685
Isosceles Triangle, 100-40-40 Degrees, Angles, Congruence.

Geometry Problem 684: Outer Nagel Point.
Triangle, Excircles, Incircle Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 683: Nagel Point.
Triangle, Excircles, Tangency points, Concurrent lines, Semi-perimeter, Ceva theorem.

Geometry Problem 682: Gergonne External Point.
Triangle, Excircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Geometry Problem 681: Gergonne Point.
Triangle, Incircle, Tangency points, Concurrent lines, Semiperimeter, Ceva theorem.

Geometry Problem 679.
Triangle, Circle, Median, Proportion.

Geometry Problem 678.
Triangle, Simson Line, Circumcircle, Tangent, Parallel, Perpendicular, Collinear Points.

Geometry Problem 674.
Triangle, Altitude, Angles.

Geometry Problem 673.
Internally tangent circles, Chord, Tangent, Metric Relations.

Geometry Problem 671.
Triangle, Cevian, Angles, Congruence.

Geometry Problem 670.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Congruence.

Geometry Problem 669.
Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map.

Geometry Problem 664.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Angles, Triangle centers.

Geometry Problem 663.
Scalene Triangle, 60 Degrees, Altitude, Angle Bisector, Perpendicular Bisector Concurrent lines.

Geometry Problem 662.
Triangle, Incenter, Circumcenter, Orthocenter, Circle, Angle, Measurement.

Geometry Problem 660.
Triangle, Circle, Diameter, Perpendicular Lines.