Congruence - Table of Content

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Kaleidoscope Index.

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

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

Symmetry (1966). Greatest film, a fantasy of dancing images breaking apart, spinning, and converging. Produced by the University of Washington, the Commission on College Physics, and the Polytechnic Institute of Brooklyn.

Semiperimeter and excircles of a triangle.

Semiperimeter and incircle of a triangle.

Semiperimeter, incircle and excircles of a triangle.

Parallelogram with Squares theorem Thébault's Theorem.
 

Johnson's Theorem. Three equal circles pass through a common point... Introduction with animation.
 

Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and trisection points of the edges.

Van Aubel's Theorem. Quadrilateral with Squares. Proof with animation.
 

Langley's Problem Adventitious angles. 20° isosceles triangle with animation.
 

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

Proposed Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity.

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 398.
Parallelogram, Area, Similarity, Congruence.

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

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Proposed Problem 363.
Right triangle, Congruence, Angles.

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

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

Equilic Quadrilateral.
 

Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean.

Proposed Problem 218. Right triangle, Altitude and Projections.

Proposed Problem 217. Right triangle, Altitude and Projections.

Proposed Problem 187. Right Triangle, Altitude, Incenters, Circles, Angles.

Proposed Problem 186. Right Triangle, Altitude, Incenters, Circles.

Proposed Problem 185. Trapezoid, Triangles and Angles.

Proposed Problem 184. Triangle and Angles.

Proposed Problem 158. Relation between the Circumradius, Inradius and Exradii of a triangle.

Proposed Problem 147. Quadrilateral, Area, Midpoints, Triangle.

Proposed Problem 135. Orthic Triangle, Altitudes, Perpendicular, Parallel

Proposed Problem 132.
Triangle, 60 degree, Orthocenter, Congruence, Midpoint.
 

Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

Triangle with Squares Problem

Proposed Problem 109. Angles, Right Triangle, Cevian.

Proposed Problem 107. Angles, Triangle. Cevian.

Proposed Problem 106. Angles, Triangle. Cevian.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions.

Proposed Problem 103.Equilateral Triangle Area, Interior Point, Heron's Formula.

Triangle and Squares Theorem 1: with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.

Proposed Problem 78: Angles of a Circle. Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.

Proposed Problem 65: Right Triangle, Mindpoints.

Interactive Hinged tessellation. Square tessellation - Dynamic Geometry.
Please be patient while the applet loads on your computer. This Java applet requires Java 1.3 or higher.

Archimedes' Book of Lemmas.
Proposition 5, Arbelos, Archimedean Twins.

I have used Geometry Expressions, the world's first Interactive Symbolic Geometry System, to visualize the Archimedean Twins and check out a variety of conjectures.

Proposed Problem 60: Isosceles triangle and angles.

Proposed Problem 59: Right and Equilateral Triangles, Midpoints

Proposed Problem 58: Right Triangle, Congruence, Perpendiculars.

Triangle and Squares 22
 

Triangle and Squares 20

Proposed Problem 49. Angles and right triangle.

Proposed Problem 48. Angles and triangles.

Proposed Problem 47. Angles and triangles.

Proposed Problem 46. Angles and triangles.

Proposed Problem 45. Angles and triangles.

Proposed Problem 44. Angles and triangles.

Proposed Problem 43. Angles and triangles.

Proposed Problem 42. Angles and triangles.

Proposed Problem 37.
Right Triangle, altitude, incircles, incenters, and orthocenter.

Triangle and Squares 16

Triangle and Squares 14

Triangle and Squares 13

Triangle and Squares 12

Triangle and Squares 11

Triangle and Squares 10

Triangle and Squares 9

Triangle and Squares 8

Triangle and Squares 7

Triangle and Squares 6

Triangle and Squares 5

Triangle and Squares 4

Triangle and Squares 3

Triangle and Squares 2

Triangle and Squares 1

Proposed Problem 34.
Right triangle, cevian, incircles, tangents and inradius.

Problem 32.
Triangle, Cevian, Incircles, Tangents.

Problem 31. Right Triangle, Incircle, Collinears.
Problem 30. Right Triangle, Incircle, Inradius.

Proposed Problem 29.
Right Triangle, altitude, incircle and inradius. Ten conclusions.

Problem 29: Geometry Help.
Facts you should know.

Proposed Problem 28
Right Triangle, altitude, incircles and inradius.

Proposed Problem 26
Right Triangle, altitude, incircles and inradius.

Proposed Problem 25
Right Triangle, altitude, incircles and inradius.

Proposed Problem 23
Right Triangle, altitude, incircles and inradii.

Proposed problem 19
Right Triangle and Excenter

Proposed Problem 17.
Right triangle, altitude, and angles.

Proposed Problem 16.
Triangle, cevian, perpendicular, and angles.

Proposed Problem 15.
Triangle, cevian, sum of segments, and angles.

Proposed Problem 14.
Triangle, median, and angles.

Proposed Problem 13. Triangle, cevian, equal segments, and angles.

Proposed Problem 12.
Triangle, cevian, equal segments, and angles.

Proposed Problem 11.
Right triangle, cevian, and angles.

Proposed Problem 10.
Triangle, cevian, equal segments, and angles.

Proposed Problem 9.
Triangles, equal segments, and angles.

Proposed Problem 8.
Triangles, equal segments, and angles.

Proposed Problem 7.
Triangle, cevian, equal segments, and angles.

Proposed Problem 6.
Triangle, cevian, equal segments, and angles.

Proposed Problem 5.
Triangle, cevian, equal segments, and angles.

Proposed Problem 4.
Quadrilateral, equal sides and angles.

Proposed Problem 3.
Triangle, median and angles.

Proposed Problem 2.
Triangle and angles.

Geometry Help: Key theorems
or Facts you should know for the proposed problems.

Proposed Problem 1.
Triangle, median and angles.