Quadrilaterals, Theorems and Problems Index. Page 6 of 6

Go Geometry: Quadrilaterals

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

Quadrilaterals: Table of Content (Page 6 of 6)

Quadrilateral Index

Trapezoid, Triangle, Area

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

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

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

Geometry Problem: Parallelogram, Triangles, Pentagon, Area

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

Geometry Problem: Parallelogram, Triangles, Area

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

Geometry Problem: Parallelogram, Triangles, Area

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

Elearning 165: Parallelogram area

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

Elearning 164: Parallelogram, Triangles, Area

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

Elearning 163 Trapezoid, Triangles, Area

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

Elearning 162 Parallelogram and Triangles Areas

Proposed Problem 162. Parallelogram, Triangles, Areas.

Elearning 161 Parallelogram and Octagon Areas

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

Circumscribed quadrilateral

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

Circumscribed Quadrilateral

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

Quadrilateral area, trisection

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

Machu Picchu

Machu Picchu and Golden Rectangle.

Quadrilateral area, trisection

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

Quadrilateral Area, Midpoint, Elearning

Proposed Problem 149. Quadrilateral, Area, Midpoints.

Quadrilateral area, Midpoint, Elearning

Proposed Problem 148. Quadrilateral, Area, Midpoints.

Quadrilateral Area, Elearning

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

Quadrilateral Area, Midpoint

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

Elearning 139: Triangle Area

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

Geometry Problem 137

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

Trapezoid

Trapezoid, Triangle, Diagonals, Midpoints. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Four Circles Theorem Using Interactive Dynamic Software
Step-by-Step construction, Manipulation, and animation. Cyclic Quadrilateral.

Pythagoras curiosity. Online tutoring.

The Pythagorean Curiosity Triangles and squares, fifteen conclusions

Inca Skull Surgery

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

Triangle Square Theorem 1. Elearning, Online Tutoring

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

Bottema Theorem. Elearning.

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

Eight Point Circle Theorem. Elearning

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

Complete quadrilateral: ortholine, Elearning

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

Elearning 96

Parallelogram Problem 96. Similar Triangles, Incenters, Parallelogram.

Elearning 93 Parallelogram

Parallelogram Problem 93. Similar Triangles, Circumcircles, Parallelogram.

Geometry problem

Proposed Problem 90. Quadrilateral and Triangle Areas, Midpoints.

Math problem

Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.

Quadrilateral area problem

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

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

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

Math Problem 77 Angles

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
Step-by-Step 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 Theorem 

Casey's Theorem. Generalized Ptolemy's Theorem.

Proposed Problem 57 

Proposed Problem 57: Angle bisector, circles Cyclic Quadrilateral.

Proposed Problem 55 

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

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, 1864-1933) 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.

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Last updated: May 7, 2009