Welcome to Theorems and Problems about Quadrilaterals! Site created and maintained by Antonio Gutierrez.

Go Geometry from the Land of the Incas. Machu Picchu and Inca Trail

The Incas used trapezoids for all their windows and doors, which withstand earthquakes well.

Quadrilaterals: Table of Content

 

 

51.

Pythagoras curiosity. Online tutoring.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions

50.

Triangle Square Theorem 1. Elearning, Online Tutoring

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

49.

Bottema Theorem. Elearning.

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

48.

Eight Point Circle Theorem. Elearning

Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.

47.

Complete quadrilateral: ortholine, Elearning

Complete Quadrilateral: Ortholine-Steiner Line.
Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation

46.

Elearning 96

Parallelogram Problem 96. Similar Triangles, Incenters, Parallelogram.

45.

Elearning 93 Parallelogram

Parallelogram Problem 93. Similar Triangles, Circumcircles, Parallelogram.

44.

Geometry problem

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.

43.

Math problem

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.

42.

Quadrilateral area problem

Proposed Problem 87. Area of Quadrilaterals and Midpoints of Diagonals.

41.

Complete quadrilateral
Newton's Theorem, Newton-Gauss Line: Complete quadrilateral theorem. Using TracenPoche Dynamic Geometry Software, Online Step-by-Step construction, manipulation, and animation.

40.

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

39.

Math Problem 77 Angles

Cyclic quadrilateral
Proposed Problem 77: Angles of a Circle. Parallel lines, Cyclic quadrilateral.

38.

Square
Proposed Problem 76: Area of a Circle
. Square, Circle, Circular Sector. 

37.

Proposed Problem 74: Three Intersecting Circles. Cyclic quadrilateral, Angles.

36.

Proposed Problem 73: Three Intersecting Circles. Cyclic quadrilateral.

 

35.

Proposed Problem 72: Intersecting Circles. Cyclic quadrilateral, Chords, Parallel.

 

34.

Proposed Problem 71: Cyclic Quadrilateral.

 

33.

Proposed Problem 70: Squares inscribed in a triangle, Similarity.

 

32.

Proposed Problem 69: Square inscribed in a triangle, Similarity.

 

31.

Proposed Problem 67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.
 

30.

Four Circles Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.

29.

Proposed Problem 63: Heptagon Regular, Side and Diagonals.

28.

Proposed Problem 62: Square Diagonal, Inscribed Circle.

27.

 

Arbelos, Inscribed Circle and Concyclic Points Cyclic Quadrilateral.

26.

Casey Theorem 

Casey's Theorem. Generalized Ptolemy's Theorem.

25.

Proposed Problem 57 

Proposed Problem 57: Angle bisector, circles Cyclic Quadrilateral.

24.

Proposed Problem 55 

Proposed Problem 55: Angle bisector, circles Cyclic Quadrilateral.

23.

Generalizing Van Aubel: Michael de Villiers' Theorems.
 

22.

Triangle and Squares. 21 theorems. Visual illustrations.

21.

Eyeball Theorem: Animated Angle to Geometry Study.

20.

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,

19.

Hippocrates and Squaring the Circle
 

18.

Triangle with Squares Problem

17.

Thébault's Theorem. Parallelogram with Squares theorem
 

16.

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

 

15.

Van Aubel

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

14.

Equilic Quadrilateral.
 

13.

Ptolemy's Theorem.
 

12.

Cyclic Quadrilateral: Ratio of the Diagonals
 

11.

Brahmagupta's Theorem Cyclic quadrilateral.

10.

Brahmagupta's Corollary Cyclic quadrilateral.

9.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

8.

Brahmagupta Formula Extension Area of any quadrilateral.

7.

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.

6.

Sangaku Problem. The incenters of four triangles in a cyclic quadrilateral form a rectangle.

5.

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,

4.

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.
 

3.

Proposed Problem 33.
Triangle and quadrilateral.

2.

Proposed Problem 35.
Incenters and Inradii in Cyclic Quadrilateral.

1.

Proposed Problem 42. Angles and triangles.

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Last updated: May 1, 2008