Quadrilaterals: Theorems and Problems
6
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Proposed Problem 170. Trapezoid,
Midpoint, Triangle, Area.
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Proposed Problem 169.
Parallelogram, Interior and Exterior Points, Diagonals, Pentagon,
Triangles, Areas
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Proposed Problem 168.
Parallelogram, Diagonal, Triangles, Pentagon, Areas.
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Proposed Problem 167.
Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem 166.
Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem 165.
Parallelogram, Diagonal, Triangles, Areas.
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Proposed Problem 164.
Parallelogram, Trapezoid, Diagonal, Triangles, Areas.
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Proposed Problem 163. Trapezoid,
Diagonals, Triangles, Areas.
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Proposed Problem 162.
Parallelogram, Triangles, Areas.
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Proposed Problem 161.
Parallelogram, Midpoints, Octagon, Areas.
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Proposed Problem 153.
Circumscribed Quadrilateral, Diagonals Concurrent with Chords.
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Proposed Problem 152.
Circumscribed Quadrilateral, Diagonal, Chord, Proportion.
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Proposed Problem 151.
Quadrilateral, Area, Trisection of Sides.
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Machu Picchu and Golden Rectangle.
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Proposed Problem 150.
Quadrilateral, Area, Trisection of Sides.
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Proposed Problem 149.
Quadrilateral, Area, Midpoints.
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Proposed Problem 148.
Quadrilateral, Area, Midpoints.
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Proposed Problem 147.
Quadrilateral, Area, Midpoints, Triangle.
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Proposed Problem 146. Varignon's
Theorem: Quadrilateral, Midpoints, Parallelogram, Area, Perimeter. |
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Proposed Problem 139. Triangle
Area, Orthic Triangle, Semiperimeter, Circumradius. |
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Proposed Problem 137.
Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points,
Parallelogram. |
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Trapezoid, Triangle, Diagonals, Midpoints.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
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Four Circles Theorem Using Interactive Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Cyclic Quadrilateral. |
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The Pythagorean Curiosity
Triangles and squares, fifteen conclusions |
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Inca Skull Surgery
Inca Skull Surgeons Were "Highly Skilled," Study Finds.
Trepanation = square hole in the skull. |
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Triangle and Squares Theorem 1: with Interactive Geometry
Software
Step-by-Step construction, Manipulation, and animation. |
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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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Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation. |
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Complete Quadrilateral: Ortholine-Steiner Line.
Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation |
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Parallelogram Problem 96. Similar
Triangles, Incenters, Parallelogram. |
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Parallelogram Problem 93. Similar
Triangles, Circumcircles, Parallelogram. |
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Proposed Problem 90.
Quadrilateral and Triangle Areas, Midpoints.
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Proposed Problem 88. Triangle and Quadrilateral Areas, Midpoints.
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Proposed Problem 87. Area of
Quadrilaterals and Midpoints of Diagonals.
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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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Cyclic quadrilateral
Proposed Problem 78: Angles of a Circle.
Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic
quadrilateral, Congruence.
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Cyclic quadrilateral
Proposed Problem 77: Angles of a Circle.
Parallel lines, Cyclic quadrilateral.
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Square
Proposed
Problem 76: Area of a Circle.
Square, Circle, Circular Sector. |
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Proposed Problem 74: Three Intersecting Circles.
Cyclic quadrilateral, Angles.
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Proposed Problem 73: Three Intersecting Circles.
Cyclic quadrilateral.
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Proposed Problem 72: Intersecting Circles.
Cyclic quadrilateral, Chords, Parallel.
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Proposed Problem 71: Cyclic Quadrilateral.
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Proposed Problem 70: Squares inscribed in a triangle, Similarity.
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Proposed Problem 69: Square inscribed in a triangle, Similarity.
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Proposed Problem 67: Triangle, Circumcircle, Angles, Cyclic
Quadrilateral.
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Four Circles Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation. |
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Proposed Problem 63: Heptagon
Regular, Side and Diagonals.
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Proposed Problem 62: Square
Diagonal, Inscribed Circle.
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Arbelos, Inscribed Circle and Concyclic Points
Cyclic Quadrilateral. |
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Casey's Theorem. Generalized Ptolemy's Theorem. |
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Proposed Problem 57: Angle bisector, circles
Cyclic Quadrilateral. |
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Proposed Problem 55: Angle bisector, circles
Cyclic Quadrilateral. |
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Generalizing Van Aubel: Michael de Villiers' Theorems.
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Eyeball Theorem:
Animated Angle to Geometry Study.
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Hippocrates and Squaring the Circle
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Triangle with Squares
Problem
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Thébault's Theorem. Parallelogram with Squares theorem
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Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges.
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Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
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Cyclic
Quadrilateral: Ratio of the Diagonals
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Brahmagupta's Theorem
Cyclic quadrilateral.
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Brahmagupta's Corollary
Cyclic quadrilateral.
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Brahmagupta's Formula
Area of a cyclic quadrilateral.
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Brahmagupta Formula
Extension
Area of any quadrilateral.
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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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Sangaku Problem. The
incenters of four triangles in a cyclic quadrilateral form a rectangle. |
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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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Proposed Problem 33.
Triangle and quadrilateral. |
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Proposed
Problem 35.
Incenters and Inradii in Cyclic Quadrilateral. |
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Proposed Problem 42.
Angles and triangles. |
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