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Congruence - Table of
Content
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Euclid's
Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's
Elements Book. Index |
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Semiperimeter and excircles of a triangle.
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Semiperimeter and incircle of a triangle. |
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Semiperimeter, incircle and excircles of a triangle.
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Parallelogram with Squares theorem Thébault's Theorem.
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Johnson's Theorem. Three equal circles pass through a common point...
Introduction with animation.
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Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and
trisection points of the edges.
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Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
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Langley's
Problem Adventitious
angles. 20° isosceles triangle with animation.
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Equilic Quadrilateral.
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Proposed Problem
158. Relation between the Circumradius, Inradius and Exradii of a triangle.
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Proposed Problem
147. Quadrilateral, Area, Midpoints, Triangle.
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Proposed Problem
135. Orthic Triangle, Altitudes, Perpendicular, Parallel
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Proposed Problem
132.
Triangle, 60 degree, Orthocenter, Congruence, Midpoint.
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Bottema's Theorem:
Triangle and Squares with Interactive
Geometry Software
Step-by-Step construction, Manipulation, and animation. |
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Triangle with Squares Problem
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Proposed Problem
109. Angles, Right Triangle, Cevian.
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Proposed Problem
107. Angles, Triangle. Cevian.
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Proposed Problem
106. Angles, Triangle. Cevian.
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The Pythagorean Curiosity
Triangles and squares, fifteen conclusions.
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Proposed Problem
103.Equilateral Triangle Area,
Interior Point, Heron's Formula.
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Triangle and Squares Theorem 1:
with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation. |
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Proposed Problem
78: Angles of a Circle.
Perpendicular and parallel
lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.
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Proposed Problem
65: Right Triangle, Mindpoints. |
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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. |
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Archimedes' Book
of Lemmas.
Proposition 5, Arbelos, Archimedean Twins.
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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.
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Proposed Problem
60: Isosceles triangle and angles. |
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Proposed Problem
59: Right and Equilateral Triangles, Midpoints |
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Proposed Problem
58: Right Triangle, Congruence, Perpendiculars. |
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Triangle and Squares 22
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Triangle and Squares 20
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Proposed Problem 49.
Angles and right triangle.
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Proposed Problem 48.
Angles and triangles.
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Proposed Problem 47.
Angles and triangles.
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Proposed Problem 46.
Angles and triangles.
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Proposed Problem 45.
Angles and triangles.
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Proposed Problem 44.
Angles and triangles.
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Proposed Problem 43.
Angles and triangles. |
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Proposed Problem 42.
Angles and triangles. |
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Proposed Problem 37.
Right
Triangle, altitude, incircles, incenters, and orthocenter. |
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Triangle and Squares 16
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Triangle and Squares 14 |
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Triangle and Squares
13 |
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Triangle and Squares
12 |
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Triangle and Squares
11 |
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Triangle and Squares
10 |
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Triangle and Squares 9
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Triangle and Squares 8 |
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Triangle and Squares 7 |
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Triangle and Squares 6 |
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Triangle and Squares 5 |
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Triangle and Squares 4 |
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Triangle and Squares 3 |
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Triangle and Squares 2 |
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Triangle and Squares 1 |
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Proposed Problem 34.
Right
triangle, cevian, incircles, tangents and inradius. |
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Problem 32.
Triangle, Cevian, Incircles, Tangents. |
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Problem 31.
Right
Triangle, Incircle, Collinears.
Problem 30.
Right
Triangle, Incircle, Inradius. |
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Proposed
Problem 29.
Right
Triangle, altitude, incircle and inradius. Ten conclusions. |
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Problem 29:
Geometry Help.
Facts you should know. |
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Proposed Problem 28
Right
Triangle, altitude, incircles and inradius. |
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Proposed Problem 26
Right
Triangle, altitude, incircles and inradius. |
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Proposed Problem 25
Right
Triangle, altitude, incircles and inradius. |
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Proposed Problem 23
Right
Triangle, altitude, incircles and inradii. |
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Proposed problem 19
Right
Triangle and Excenter |
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Proposed
Problem 17.
Right triangle, altitude, and angles. |
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Proposed Problem 16.
Triangle, cevian, perpendicular, and angles. |
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Proposed Problem 15.
Triangle, cevian, sum of segments, and angles. |
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Proposed
Problem 14.
Triangle, median, and angles. |
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Proposed Problem 13.
Triangle, cevian, equal segments, and angles. |
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Proposed Problem 12.
Triangle, cevian, equal segments, and angles. |
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Proposed Problem 11.
Right triangle, cevian, and angles. |
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Proposed Problem 10.
Triangle, cevian, equal segments, and angles. |
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Proposed Problem 9.
Triangles, equal segments, and angles. |
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Proposed Problem 8.
Triangles, equal segments, and angles. |
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Proposed Problem 7.
Triangle, cevian, equal segments, and angles. |
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Proposed Problem 6.
Triangle, cevian, equal segments, and angles. |
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Proposed Problem 5.
Triangle, cevian, equal segments, and angles. |
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Proposed Problem 4.
Quadrilateral, equal sides and angles. |
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Proposed Problem 3.
Triangle, median and angles. |
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Proposed Problem 2.
Triangle and angles. |
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Geometry Help: Key theorems
or Facts you should know for the proposed problems. |
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Proposed Problem 1.
Triangle, median and angles. |
