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Geometry, Machu Picchu

Geometry Theorems and Problems - Recent Additions (Page 1 of 8)

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Congruence

Congruence. Index.

Similarity

Similarity, Ratios, Proportions

Areas

Areas Index.

Midpoint Theorems and Problems Index

Midpoints Index.
Theorems and Problems

Tangential or Circumscribed Quadrilateral Index, theorems and problems

Tangential or Circumscribed Quadrilateral

Altitude of a triangle

Altitude Index.
Theorems and Problems.

Collinear Points Index

Collinear Points.
Theorems and Problems

Incenter, Incircle, Index

Incenter. Index.

Polygons Index

Polygons.
Theorems and Problems.

Square, Angle trisectors

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

Median of a triangle, Index

Median Index.
Theorems and Problems.

Special Right Triangle 30-60 Index

Special Right Triangle 30-60.

Special right triangle 30 60

Special Right Triangles.

Tangent Circles Index

Tangent Circles Index

Triangle area, Circle, Curvilinear triangle

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

Right triangle, Incircle, Angle

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

Area of Triangle, Circles, Diameters

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

Cyclic quadrilateral, Rhombus

Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

Mascheroni Construction with compass alone

Mascheroni construction: Find the center of a circle with compass alone

Euclid Elements Book X, Lemma for Proposition 33

Euclid's Elements, Book X, Lemma for Proposition 33

Triangle, 120 degrees, angle bisectors

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

Eight Point Circle

Eight-Point Circle Theorem

Complete quadrilateral

Complete Quadrilateral: Ortholine-Steiner Line

Quadrilateral Area. Elearning 98

Proposed Problem 100. Circle Area, Archimedes' Book of Lemmas.

Quadrilateral Area. Elearning 98

Proposed Problem 99: Circle Area, General Extension to Pythagoras' Theorem

Math problem

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.

Math problem

Proposed Problem 89. Triangles of equal area, Midpoints.

Math Problem

Intouch and Extouch Triangles, Areas

Math Problem

Contact Triangles Areas, Incircle, Excircle

Math Problem

Area of the Contact Triangle, inradius, circumradius

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mascheroni Construction with compass alone.

 

 

 

 

 

 

Right Triangles, Formulas and Facts

Mind Map of the Pythagorean Theorem
Proofs by shears, translation, similarity. Facts.

Brahmagupta Formula Extension Area of any quadrilateral.

 

Brahmagupta's Theorem Cyclic quadrilateral.

Brahmagupta's Corollary Cyclic quadrilateral.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

 

Most Popular Videos of Geometry

Proposed Problem 50,
49, 48, 47, 46, 45, 44, 43.

Proposed Problem 42. Angles and triangles.

 

 

Sangaku Problem 41. "Mickey Mouse."

Proposed Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances.

Proposed Problem 40. Geometry Help.

 

Table of Content

  1. Triangles. Theorems and problems about triangles.

  2. Circles. Theorems and problems about circles.

  3. Triangle Centers

  4. Archimedes' Book of Lemmas

  5. Quadrilaterals

  6. Adams' Circle

  7. First Ajima-Malfatti Point

  8. Second Ajima-Malfatti Point

  9. Apollonius' Tangency Problem for Three Circles Illustration with animation and sound.

  10. The Bevan Point

  11. Blanchet Theorem

  12. Butterfly Theorem. See also: Butterfly Theorem Puzzle

  13. Carnot's Theorem

  14. Ceva's Theorem

  15. Clifford's Circles Chain Theorems

  16. Equal Incircles Theorem

  17. Equilic Quadrilateral.

  18. Euler and his beautiful and extraordinary formula that links the 5 fundamental constants e, i, Pi , 1 and 0, together!

  19. Eyeball Theorem. Illustration

  20. Gergonne Point Theorem

  21. Heron's Formula. Key facts and a purely geometric step-by-step proof.

  22. Johnson's Theorem

  23. Kurschak's Tile & Theorem

  24. Langley Problem: 20° Isosceles Triangle Adventitious angles.

  25. Lemoine Theorem Animated Angle

  26. Menelaus' Theorem

  27. Miquel's Pentagram. Proof

  28. Miquel's Pentagram. Dynamic Geometry Cabri, GSP, Cinderella, C.a.R.

  29. Monge & d'Alembert Three Circles Theorem I - Dynamic Geometry Requires Java applet 1.3 or higher.

  30. Monge & d'Alembert Three Circles Theorem II - Dynamic Geometry Requires Java applet 1.3 or higher.

  31. Morley's Theorem

  32. Napoleon's Theorem

  33. Nagel Point Theorem. See also: Nagel Point Flowchart Proof, Nagel Point Puzzle.

  34. Newton's Theorem: Newton's Line

  35. Nine-Point Center, Nine-Point Circle, Euler Line

  36. Parallelogram with Squares theorem.

  37. Pascal's Mystic Hexagram Theorem Proof

  38. Pentagons and Pentagrams. Menelaus and Collinearity

  39. Platonic Solids. Interactive animation.

  40. Poncelet's Theorem

  41. Proposed Problems about congruence of line segments, angles, and triangles. Level: High School, SAT Prep, College geometry.

  42. Ptolemy's Theorem.

  43. Ptolemy's Extension Cyclic Quadrilateral: Ratio of the Diagonals.

  44. Sangaku Problem

  45. Sangaku Problem 2

  46. Sangaku Problem 3

  47. Sawayama -Thebault's theorem

  48. Semiperimeter and excircles of a triangle

  49. Semiperimeter and incircle of a triangle

  50. Semiperimeter, incircle and excircles of a triangle

  51. Seven Circles Theorem

  52. Simson Line

  53. Simson Line: Angle between two Simson lines

  54. Steiner's Theorem

  55. 100° Isosceles Triangle Problem

  56. Taylor Circle

  57. Three Circles Theorem

  58. Three Tangent Circles Theorem

  59. Triangles

  60. Triangle with the bisectors of the exterior angles. Collinearity

  61. Triangle & squares. 22 theorems, visual illustrations.

  62. Triangle with Squares 0 Two squares.

  63. Triangle with Squares 1 Two squares.

  64. Triangle with Squares 2 Two squares.

  65. Triangle with Squares 3 Three squares.

  66. Triangle with Squares 4 Finsler-Hadwiger Theorem.

  67. Triangle with Squares 5 Two squares, median and altitude.

  68. Triangle with Squares 6 Four squares.

  69. Triangle Centers

  70. Van Aubel's Theorem Quadrilateral with Squares

  71. Generalizing Van Aubel: Michael de Villiers' Theorems.

  72. Varignon and Wittenbauer parallelograms

  73. Adjacent Angles and Five Bisectors

  74. Mind Map of How to Solve Problems
    George Pólya's 1945 book How to Solve It is a book describing methods of problem solving.

         

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