Quadrilaterals: Theorems and Problems
6




Proposed Problem 170. Trapezoid,
Midpoint, Triangle, Area.


Proposed Problem 169.
Parallelogram, Interior and Exterior Points, Diagonals, Pentagon,
Triangles, Areas


Proposed Problem 168.
Parallelogram, Diagonal, Triangles, Pentagon, Areas.


Proposed Problem 167.
Parallelogram, Diagonal, Triangles, Areas.


Proposed Problem 166.
Parallelogram, Diagonal, Triangles, Areas.


Proposed Problem 165.
Parallelogram, Diagonal, Triangles, Areas.


Proposed Problem 164.
Parallelogram, Trapezoid, Diagonal, Triangles, Areas.


Proposed Problem 163. Trapezoid,
Diagonals, Triangles, Areas.


Proposed Problem 162.
Parallelogram, Triangles, Areas.


Proposed Problem 161.
Parallelogram, Midpoints, Octagon, Areas.


Proposed Problem 153.
Circumscribed Quadrilateral, Diagonals Concurrent with Chords.


Proposed Problem 152.
Circumscribed Quadrilateral, Diagonal, Chord, Proportion.


Proposed Problem 151.
Quadrilateral, Area, Trisection of Sides.


Machu Picchu and Golden Rectangle.


Proposed Problem 150.
Quadrilateral, Area, Trisection of Sides.


Proposed Problem 149.
Quadrilateral, Area, Midpoints.


Proposed Problem 148.
Quadrilateral, Area, Midpoints.


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


Proposed Problem 146. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter. 

Proposed Problem 139. Triangle
Area, Orthic Triangle, Semiperimeter, Circumradius. 

Proposed Problem 137.
Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points,
Parallelogram. 

Trapezoid, Triangle, Diagonals, Midpoints.
Dynamic Geometry.
StepbyStep construction, Manipulation, and animation.
Prove proposition. 

Four Circles Theorem Using Interactive Dynamic Software
StepbyStep construction, Manipulation, and animation.
Cyclic Quadrilateral. 

The Pythagorean Curiosity
Triangles and squares, fifteen conclusions 

Inca Skull Surgery
Inca Skull Surgeons Were "Highly Skilled," Study Finds.
Trepanation = square hole in the skull. 

Triangle and Squares Theorem 1: with Interactive Geometry
Software
StepbyStep construction, Manipulation, and animation. 

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

EightPoint Circle Theorem
StepbyStep construction, Manipulation, and animation. 

Complete Quadrilateral: OrtholineSteiner Line.
Using TracenPoche Dynamic Software
StepbyStep construction, Manipulation, and animation 

Parallelogram Problem 96. Similar
Triangles, Incenters, Parallelogram. 

Parallelogram Problem 93. Similar
Triangles, Circumcircles, Parallelogram. 

Proposed Problem 90.
Quadrilateral and Triangle Areas, Midpoints.


Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.


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


Complete quadrilateral
Newton's Theorem, NewtonGauss Line: Complete quadrilateral theorem.
Using TracenPoche Dynamic Geometry Software,
Online StepbyStep construction, manipulation, and animation. 

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


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


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

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


Proposed Problem 73: Three Intersecting Circles.
Cyclic quadrilateral.


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


Proposed Problem 71: Cyclic Quadrilateral.


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


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


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


Four Circles Theorem Using TracenPoche Dynamic Software
StepbyStep construction, Manipulation, and animation. 

Proposed Problem 63: Heptagon
Regular, Side and Diagonals.


Proposed Problem 62: Square
Diagonal, Inscribed Circle.


Arbelos, Inscribed Circle and Concyclic Points
Cyclic Quadrilateral. 

Casey's Theorem. Generalized Ptolemy's Theorem. 

Proposed Problem 57: Angle bisector, circles
Cyclic Quadrilateral. 

Proposed Problem 55: Angle bisector, circles
Cyclic Quadrilateral. 

Generalizing Van Aubel: Michael de Villiers' Theorems.


Eyeball Theorem:
Animated Angle to Geometry Study.


Hippocrates and Squaring the Circle


Triangle with Squares
Problem


Thébault's Theorem. Parallelogram with Squares theorem


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


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


Cyclic
Quadrilateral: Ratio of the Diagonals


Brahmagupta's Theorem
Cyclic quadrilateral.


Brahmagupta's Corollary
Cyclic quadrilateral.


Brahmagupta's Formula
Area of a cyclic quadrilateral.


Brahmagupta Formula
Extension
Area of any quadrilateral.


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. 

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

Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 18641933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.


Proposed Problem 33.
Triangle and quadrilateral. 

Proposed
Problem 35.
Incenters and Inradii in Cyclic Quadrilateral. 

Proposed Problem 42.
Angles and triangles. 
Go to Page:
Previous

1 
2 
3 
4

5

6  Next
