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Quadrilaterals: Table of Content
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51. |
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The Pythagorean Curiosity
Triangles and squares, fifteen conclusions |
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50. |
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Triangle and Squares Theorem 1:
with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation. |
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49. |
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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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48. |
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Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation. |
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47. |
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Complete Quadrilateral: Ortholine-Steiner Line.
Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation |
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46. |
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Parallelogram Problem
96. Similar Triangles, Incenters, Parallelogram.
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45. |
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Parallelogram Problem
93. Similar Triangles, Circumcircles, Parallelogram.
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44. |
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Proposed Problem
90. Quadrilateral and Triangle
Areas, Midpoints.
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43. |
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Proposed Problem
88. Triangle and Quadrilateral Areas, Midpoints.
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42. |
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Proposed Problem
87. Area of Quadrilaterals and Midpoints of Diagonals.
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41. |
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Complete quadrilateral
Newton's
Theorem, Newton-Gauss Line: Complete quadrilateral theorem. Using TracenPoche Dynamic
Geometry Software, Online
Step-by-Step construction, manipulation, and animation. |
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40. |
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Cyclic quadrilateral
Proposed Problem
78: Angles of a Circle.
Perpendicular and parallel
lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.
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39. |
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Cyclic quadrilateral
Proposed Problem
77: Angles of a Circle. Parallel
lines, Cyclic quadrilateral.
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38. |
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Square
Proposed Problem
76: Area of a Circle. Square,
Circle, Circular Sector. |
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37. |
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Proposed Problem
74: Three Intersecting Circles. Cyclic
quadrilateral, Angles.
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36. |
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Proposed Problem
73: Three Intersecting Circles. Cyclic
quadrilateral.
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35. |
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Proposed Problem
72: Intersecting Circles. Cyclic
quadrilateral, Chords, Parallel.
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34. |
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Proposed Problem
71: Cyclic Quadrilateral.
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33. |
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Proposed Problem
70: Squares inscribed in a triangle, Similarity.
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32. |
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Proposed Problem
69: Square inscribed in a triangle, Similarity.
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31. |
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Proposed Problem
67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
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30. |
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Four Circles
Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation. |
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29. |
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Proposed Problem 63: Heptagon Regular, Side and Diagonals.
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28. |
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Proposed Problem 62: Square Diagonal, Inscribed Circle.
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27. |
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Arbelos,
Inscribed Circle and Concyclic Points Cyclic
Quadrilateral. |
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26. |
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Casey's Theorem. Generalized Ptolemy's Theorem. |
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25. |
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Proposed Problem
57: Angle bisector, circles Cyclic
Quadrilateral. |
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24. |
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Proposed Problem
55: Angle bisector, circles Cyclic
Quadrilateral. |
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23. |
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Generalizing Van Aubel: Michael de Villiers' Theorems.
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22. |
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Triangle and Squares. 21
theorems. Visual illustrations. |
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21. |
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Eyeball Theorem:
Animated Angle to Geometry Study.
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20. |
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Eyeball to Eyeball Theorem
Presentation: "Animated
Angle to Geometry Study I & II." 46th
Annual Georgia Mathematics Conference, Extreme Makeover: Mathematics
Edition!, Rock Eagle, October 20-22, 2005, |
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19. |
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Hippocrates and Squaring the Circle
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18. |
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Triangle with Squares Problem
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17. |
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Thébault's Theorem. Parallelogram with Squares theorem
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16. |
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Varignon and Wittenbauer paralellograms. Quadrilateral: midpoints and
trisection points of the edges.
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15. |
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Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
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14. |
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Equilic Quadrilateral.
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13. |
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Ptolemy's Theorem.
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12. |
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Cyclic
Quadrilateral: Ratio of the Diagonals
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11. |
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Brahmagupta's Theorem
Cyclic quadrilateral.
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10. |
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Brahmagupta's Corollary
Cyclic quadrilateral.
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9. |
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Brahmagupta's Formula
Area of a cyclic quadrilateral.
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8. |
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Brahmagupta Formula Extension
Area of any quadrilateral.
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7. |
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Newton's
Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of
diagonals, center of the circle inscribed.
Puzzle of the Newton's Theorem:
50 pieces of circles. |
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6. |
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Sangaku Problem. The incenters of four
triangles in a cyclic quadrilateral form a rectangle. |
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5. |
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Complete Quadrilateral Theorems
Presentation: "Animated
Angle to Geometry Study I & II." 46th
Annual Georgia Mathematics Conference, Extreme Makeover: Mathematics
Edition!, Rock Eagle, October 20-22, 2005, |
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4. |
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Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.
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3. |
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Proposed Problem 33.
Triangle and quadrilateral. |
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2. |
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Proposed Problem 35.
Incenters and Inradii in Cyclic Quadrilateral. |
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1. |
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Proposed Problem 42.
Angles and triangles. |
